Transfer of impurities into crystals in industrial processes: … · 2017-08-28 · Vasanth Kumar...

Transfer of impurities into crystals in industrial processes: Mechanism and kinetics

Vasanth Kumar Kannuchamy

A thesis submitted in part fulfillment of the requirement for the degree of Doctor in the

Faculty of Engineering, University of Porto, Portugal

This thesis was supervised by Prof. Fernando Alberto Nogueira da Rocha and Dr. Pedro

Miguel da Silva Martins. Departamento de Engenharia Química, Faculdade de

Engenharia da Universidade do Porto, Porto, Portugal

Departamento de Engenharia Química Faculdade de Engenharia da Universidade do Porto

Porto, Portugal

2010

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AbstractAbstractAbstractAbstract

Batch experiments were carried out to study the effect of Hodag CB6, a non-ionic

surfactant, on the overall growth kinetics of sucrose crystals as a function of

supersaturation and impurity concentration at 30 and 50 oC. The kinetics and

thermodynamics of the overall growth process was analyzed using multiple nucleation,

Burton-Cabrera-Frank (BCF) surface diffusion and a recently introduced spiral

nucleation models. The growth promoting effect of the added impurity was due to the

decrease in surface energy induced by the added surfactant. The surface free energy

calculated by these models was found to be globally decreasing with increasing surfactant

concentration at the studied temperatures. All these models suggested that the growth

process was influenced by both kinetic and thermodynamic effect, the later effect being

predominant. The coverage of impurity molecules on the sucrose surface followed a

Henry type expression according to Langmuir isotherm at the studied temperatures. In the

case of pure system, the total kink density was estimated as 1015 and 1016 kinks/m2 by

multiple nucleation and spiral nucleation model respectively. The mean linear growth rate

of sucrose crystals in pure solutions was found to 5.58 x 109 and 1.36 x 1010 crystal

monolayers/s at 30 and 50 oC, respectively. The active growth sites on the crystal surface

were found to be 2 to 3 orders of magnitude less than the total number of sucrose

molecules.

In addition to the studies about the kinetics and thermodynamics of overall growth

process, growth kinetics of individual faces of the sucrose crystals were studied using a

well established image analysis technique. The morphological parameters determined by

image analysis were used to study the growth kinetics and thermodynamics of (110),

(001) and (100) faces and also to quantify the agglomeration effect of the added impurity.

The kinetics and thermodynamics of the growing faces was studied using a multiple

nucleation model and BCF surface diffusion model. The coverage of impurity molecules

onto (110), (001) and (100) faces followed a Langmuir isotherm with affinity coefficient

of 0.143 L/g, 0.180 L/g and 0.180 L/g, respectively. The differential heat of adsorption of

impurity onto sucrose surface, Qdiff, was found to be around 20 kJ/mol. The activation

iv

energy for the growth process in pure and impure solutions by a multiple nucleation

model was found to be 67-68 kJ/mol and 68-69 kJ/mol, respectively.

A section of this thesis discusses our second principle objective that deals about

the effect of added surfactants on the surface properties of sucrose in detail using inverse

gas chromatography (IGC) experiments. IGC experiments were performed with pure

sucrose crystals, surfactant coated crystal and crystals grown in the presence of surfactant

at 313.05 and 323.05 K. The surfactant promotes the specific interactions with the polar

probes. The sorption of basic, acidic and amphoteric probes onto pure and surfactant

coated sucrose was found to be endothermic and in the case of neutral probes was found

to be exothermic. The surfactant increases both the acidity and basicity of the sucrose

surface with latter effect being significant. The role of interfacial tension on the growth

kinetics of sucrose crystals was studied using IGC for different surfactant concentrations.

IGC results with the surfactant coated sucrose were used to interpret the thermodynamic

effect of surfactants during the crystal growth process. The dispersive component of the

surface energy of the surfactant coated sucrose crystals was found to be lower than that of

pure sucrose crystals and was found to be in the range of 33.49 to 35.27 mJ/m2.

Finally an attempt was made to explain the change in activity of dislocation

spirals on the surfaces of crystal collective during a crystal growth process in diffusion

and in kinetic regime. The model was proposed assuming that the change in activity of

crystals decreases with time (i.e., changing supersatruation) and follows a first order

kinetics irrespective of the growth process in diffusion or in kinetic regime. The proposed

model was fitted to explain the experimental growth kinetics of sucrose in solutions at

different temperatures and agitation speeds. The proposed model well represents the

experimental data for the range of experimental conditions studied. The proposed model

is very simple to use and for the first time incorporates the parameter to explain the

change in activity of dislocation spirals during a crystal growth process. The proposed

models have the advantage to estimate the kinetic constant of the growth process and the

rate of change in activity of dislocation spirals on the crystals surface simultaneously.

The total energy of adsorption for the growth of sucrose crystals was determined using

the proposed model and found to be 93 and 92 kJ/mol at 30 and 40 oC, respectively.

v

ResumoResumoResumoResumo

Realizaram-se experiências “batch” para estudar o efeito de Hodag CB6, um agente

tensioactivo não-iónico, na cinética de crescimento de cristais de açúcar, como função da

sobressaturação e concentração da impureza, a 30 e 50 ºC. A cinética e termodinâmica do

processo de crescimento global foi analisado usando um modelo de nucleação múltipla, o

modelo de difusão à superfície de Burton, Cabrera e Frank (BCF), e o modelo de

nucleação em espirais recentemente apresentado. O efeito promotor de crescimento

cristalino da impureza adicionada foi devido à diminuição da energia superficial induzida

pela impureza. Apurou-se que a energia livre superficial calculada por estes modelos

diminui globalmente com o aumento da concentração do agente tensioactivo, às

temperaturas estudadas. Todos estes modelos sugerem que o processo de crescimento foi

influenciado por ambos os efeitos, cinético e termodinâmico, sendo este último efeito

predominante. A adsorção das moléculas de impureza na superfície de sacarose, às

temperaturas estudadas, segue uma expressão tipo de Henry, de acordo com a isotérmica

de Langmuir. No caso do sistema puro, a densidade total de “kinks” foi estimada como

1015 e 1016 “kinks”/m2, através do modelo de nucleação múltiplo e de nucleação em

espiral, respectivamente. A velocidade de crescimento linear média dos cristais de

sacarose em soluções puras é 5.58 x 109 e 1.36 x 1010 monocamadas/s a 30 e 50 ºC,

respectivamente. Os sítios de crescimento activos na superfície do cristal foram

estimados ser 2 a 3 ordens de grandeza menores que o número total de moléculas de

sacarose.

Além do estudo cinético e termodinâmico do processo global, determinaram-se, também,

as cinéticas de crescimento de faces dos cristais de sacarose, usando uma técnica de

análise de imagem. Os parâmetros morfológicos determinados por esta técnica foram

usados para estudar a cinética de crescimento e termodinâmica das faces (110), (001) e

(100), e, também, para quantificar o efeito sobre a aglomeração da impureza adicionada.

A cinética e termodinâmica das faces em crescimento foram estudadas usando um

modelo de nucleação múltiplo e o modelo de difusão à superfície BCF. A adsorção da

impureza nas faces (110), (001) e (100) segue uma isotérmica de Langmuir com um

coeficiente de 0.143, 0.180 e 0.180 L/g, respectivamente. O calor de adsorção diferencial

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da impureza na superfície de sacarose, Qdiff, foi estimado ser aproximadamente 20

kJ/mol. A energia de activação para o processo de crescimento em soluções puras e

impuras situou-se em 67-68 e 68-69 kJ/mol, respectivamente.

Uma secção desta tese discute um segundo objectivo deste trabalho que trata do efeito do

agente tensioactivo nas propriedades de superfície da sacarose usando a técnica da

cromatografia inversa (IGC). Foram realizados ensaios com cristais de sacarose pura,

cristais cobertos com agente tensioactivo e cristais que cresceram na presença de

impureza a 313.05 e 323.05 K. A impureza promove as interacções específicas com

compostos polares. Apurou-se que a adsorção de compostos alcalinos, ácidos e

anfotéricos em cristais cobertos com impureza é endotérmica, e no caso de compostos

neutros exotérmica. O agente tensioactivo aumenta tanto a acidez e alcalinidade da

superfície de sacarose com o último efeito a ser dominante. O papel da tensão interfacial

na cinética de crescimento dos cristais de sacarose foi estudado para diferentes

concentrações da impureza. Os resultados de IGC com os cristais cobertos com impureza

foram usados para interpretar o efeito termodinâmico da impureza durante o processo de

crescimento. A componente dispersiva da energia de superfície dos cristais cobertos com

impureza situou-se abaixo da dos cristais puros, encontrando-se na gama de 33.49 a 35.27

mJ/m2.

Finalmente, fez-se uma tentativa para explicar a variação da actividade das espirais

resultantes de “deslocações“ na superfície dos cristais num processo de crescimento

cristalino. O modelo proposto assume que essa variação segue uma cinética de primeira

ordem, independentemente de estarmos em regime difusional ou cinético. Este modelo

ajusta-se bem aos resultados experimentais obtidos para as diferentes temperaturas e

velocidades de agitação estudadas. O modelo é muito simples e procura estimar o

parâmetro cinético e a variação da actividade das espirais na superfície dos cristais,

simultaneamente. A energia total de adsorção no crescimento de cristais de sacarose foi

determinada por este modelo, encontrando-se os valores de 93 e 92 kJ/mol nas

experiências realizadas a 30 e 40 ºC, respectivamente.

vii

Résumé Résumé Résumé Résumé

Expériences batch ont été réalisées pour étudier l'effet de Hodag CB6, un agent

tensioactif non ionique, sur la cinétique de croissance global de cristaux de saccharose en

fonction de la sursaturation et la concentration d'impureté à 30 et 50 ºC. La cinétique et la

thermodynamique du processus de croissance globale a été analysée à l'aide d’un modèle

de nucléation multiple, du modèle de diffusion de surface de Burton-Cabrera-Frank

(BCF) et d'un modèle de nucleation en spirale récemment introduit. L'effet de la

promotion de la croissance de l'impureté ajoutée est due à la diminution de l'énergie de

surface induit par l'agent tensioactif ajouté. La surface d'énergie libre, calculé par ces

modèles a été jugée globalement décroissante avec l'augmentation de concentration de

surfactant, aux températures étudiées. Tous ces modèles ont suggéré que le processus de

croissance a été influencée par l'effet cinétique et thermodynamique, l'effet dominant

étant celui-ci. La couverture des molécules d'impureté sur la surface de saccharose suivi

une expression de type Henry en fonction de l'isotherme de Langmuir dans les

températures étudiées. Dans le cas du système pur, la densité des “kink” a été estimé à

1015 et 1016 kinks/m2 par nucléation multiple et le modèle de nucléation spirale,

respectivement. Le taux moyen de croissance linéaire de cristaux de saccharose en

solution pure a été retrouvé à 5,58 x 109 et 1,36 x 1010 monocouches de crystal/s à 30 et

50 ºC, respectivement. Les sites de croissance active sur la surface du cristal se sont

révélés être de 2 à 3 ordres de grandeur inférieur que le nombre total de molécules de

saccharose.

En plus des études sur la cinétique et thermodynamique des processus de croissance

globale, la cinétique de croissance de faces différents des cristaux de saccharose ont été

étudiés en utilisant une technique bien établie, l’analyse d'image. Les paramètres

morphologiques déterminée par analyse d'image ont été utilisés pour étudier la cinétique

de croissance et la thermodynamique des faces (110), (001) et (100) et également de

quantifier l'effet d'agglomération des impuretés ajoutés. La cinétique et la

thermodynamique des faces de croissance a été étudiée en utilisant le modèle de

nucléation multiple et le modèle de diffusion de surface BCF. La couverture des

molécules d'impureté sur (110), (001) et (100) faces suivi une isotherme de Langmuir

viii

avec un coefficient d’ affinité de 0,143, 0,180 et 0,180 L/ g, respectivement. La chaleur

différentielle d'adsorption des impuretés sur la surface de saccharose, Qdiff, a été trouvé

être dans la gamme de 17-18 kJ/mol. L'énergie d'activation pour le processus de

croissance dans les solutions pur et impur, par le modèle de nucléation multiple, a été

jugée 67-68 kJ/mol et 68-69 kJ/mol, respectivement.

Une section de cette thèse traite de notre second objectif qui porte sur l'effet des agents

tensioactifs ajoutés sur les propriétés de surface de saccharose en utilisant la

chromatographie gazeuse inverse (IGC). Expériences ont été réalisées avec des cristaux

de saccharose pur, cristaux couvert avec l’agent tensioactif et cristaux cultivés en

présence de tensioactif, à 313,05 et 323,05 K. Le surfactant favorise les interactions

spécifiques avec les sondes polaires. L'adsorption des sondes basiques, acides et

amphotères sur saccharose pur et couvert de l’agent tensioactif était jugée endothermique

et dans le cas des sondes neutre, exothermique. L'agent tensioactif augmente l'acidité et la

basicité de la surface, le dernier effet étant importante. Le rôle de la tension interfaciale

sur la cinétique de croissance de cristaux de saccharose a été étudiée pour différentes

concentrations de l'agent tensioactif. Les résultats dês cristaux couvert d’agent tensioactif

ont été utilisés pour interpréter le effet thermodynamique pendant le processus de

croissance des cristaux. La composante dispersive de l'énergie de surface des cristaux de

saccharose couvert d’agent tensioactif a été jugée inférieure à celle des cristaux de

saccharose pur étant dans la gamme de 33,49 à 35,27 mJ/m2.

Une tentative a été faite pour expliquer le changement dans l'activité des défauts

cristallins de spirales sur les surfaces des cristaux pendant le processus de croissance

cristalline, à différentes températures et vitesse d'agitation. Le modèle a été proposé en

supposant que le changement dans l'activité de cristaux diminue avec le temps, étant le

régime diffusionnel ou cinétique. Le modèle proposé représente bien les données

expérimentales pour la gamme de conditions expérimentales étudiées. Le modèle proposé

est très simple à utiliser et a l'avantage d'estimer la constante cinétique du processus de

croissance et le taux de variation de l'activité de spirales sur la surface du cristal, en

même temps. L'énergie totale de l'adsorption pour la croissance de cristaux de saccharose

a été déterminée selon le modèle proposé et a été retrouvé à 93 et 92 kJ/mol à 30 et 40 ºC.

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Dedicated to my parents and to my brother in love and gratitude

xi

AcknowledgementsAcknowledgementsAcknowledgementsAcknowledgements

I would like to express my sincere gratitude to my principle advisor, Prof. Fernando Rocha for

introducing me to the field of crystallization as well as for supporting and guiding me throughout

the entire research. It has been a memorable learning journey for me with him and I will cherish

the memories for the years to come. I would also like to thank my co-supervisor Dr. Pedro

Martins for his help.

I would like to acknowledge the support and resources provided by the Department of

Chemical Engineering, University of Porto, throughout the study. I would like to extend my

thanks to Fundação para a Ciência e Tecnologia (FCT), Portugal, for the scholarship grant

(PTDC/EQU-FTT/81496/2006). I take this opportunity to thank the Director of FEUP for giving

fifty percent reduction of my first and third year tuition fees.

Sincere and special thanks to one of my colleagues Dr. Antonio Ferreira, who helped me

right from the first day by many means and also for teaching me experimental and image analysis

techniques.

I need to mention my colleague and friend, Issam Ali Khaddour for the unexpected

friendship and also for some of his stimulating questions that ignited some ideas in my mind

during data interpretations.

My sincere thanks are extended to my other colleagues Berta, Cecília and José for their

friendship and kindness.

I am at loss of words for the kindness of my friends and well wishers Olinda, Patrícia,

Carla, my Brazil mother, Julcy and every one in my residence who always made me to feel the

home and for their love and caringness during my entire stay in Porto.

I would like to give my thanks with deepest emotions to my best friend Teddy for his

moral support and spiritual words that recovered me from depressions many times.

I am sure I will never find a word in any languages I know to express the thanks for the

support and blessings of my parents which make to achieve everything I got now in this life. I

would like to show my respect and love to them by dedicating this thesis for them.

K. Vasanth Kumar

xiii

ContentsContentsContentsContents

Abstract iii

Resumo v

Résumé vii

Acknowledgements xi

Notations xvii

List of figures xxiii

List of tables xxvii

Chapter 1 Growth of crystals in impure solution: An introduction 1

Abstract 1

1.1. Crystallization 1

1.2. Motivation and Objectives 2

1.3. Structure of the thesis 4

1.4. References 6

Chapter 2 Effect of Impurities on Crystal Growth Kinetics: Theories 9

Abstract 9

2.1. Growth Models 10

2.1.1. Layer growth of F faces 11

2.1.1.1. Mononuclear model 11

2.1.1.2. Polynuclear model 12

2.1.1.3. Birth and Spread model 12

2.1.2. Two dimensional nucleation models with surface diffusion and two

dimensional models with direct integration

13

2.1.3. Spiral growth models 14

2.1.4. Spiral nucleation model 16

2.1.5. Adsorption of impurities on F faces: Kinetic models 17

2.1.5.1. Cabrera and Vermilyea model (1958) 18

2.1.5.2. Kubota-Mullin model (2000) 18

xiv

2.1.5.3. Competitive sorption model (Martins et al., 2006) 20

2.2. References 21

Chapter 3 Batch Crystal Growth Experiments in Pure and Impure Solutions 23

3.1. Sucrose 23

3.2. Surfactant 23

3.3. Crystal growth experiments 23

3.4. Image analysis 25

3.5. References 26

Chapter 4 Studies on the effects of a non-ionic surfactant on the growth

kinetics of sucrose crystals

27

Abstract 27

4.1. Introduction 27

4.2. Experimental 29

4.3. Results and discussions 29

4.3.1. Multiple nucleation model 34

4.3.2. BCF surface diffusion model 46

4.4. Conclusions 54

4.5. References 56

Chapter 5 Kinetics and thermodynamics of sucrose crystal growth in the

presence of a non-ionic surfactant according to a spiral nucleation model

59

Abstract 59



5.3. Results and discussion 61

5.4. Conclusions 73

5.5. References 75

Chapter 6 On the effect of a non-ionic surfactant on the surface of sucrose

crystals and on the crystal growth process by inverse gas chromatography

79

Abstract 79


xv


6.2.1. Crystal growth experiments 81

6.2.2. Sucrose sample preparation 81

6.2.3. IGC experiments 81

6.3. Results and Discussion 84

6.4. Conclusions 101

6.5. References 102

Chapter 7 Kinetic, thermodynamic and agglomeration effect of impurity in a

crystal growth process using image analysis

105

Abstract 105


7.2. Materials and Methods 107

7.2.1. Experimental 107

7.2.2. Image analysis 107

7.3. Results and Discussions 109

7.3.1. Quantifying agglomeration 109

7.3.2. Face growth kinetics and thermodynamics 112

7.3.2.1. Multiple nucleation model 117

7.3.2.2. Burton-Cabrera-Frank model 127


7.5. References 133

Chapter 8 A simple model to explain the rate of change in dislocation activity

of the crystal surfaces of crystal collective during a growth process in a batch

crystallizer

137

Abstract 137



8.2.1. Sucrose 139

8.2.2. Crystal growth experiments 139

8.3. Results and discussions 139

xvi


8.5. References 149

Chapter 9 Contributions of the present research and few suggestions for future

work

151

xvii

NotationsNotationsNotationsNotations

A total surface area on a crystal surface, m2

A’ constant (in Eq. (2.9))

AJ new nuclei formed per unit time

Am area occupied by one molecule

AN* corrected Gutmann’s acceptor number, J/mol

Ao kinetic coefficient, m/s

sucroseA area occupied by one sucrose molecule, m2

Atot total surface area of the sucrose crystals available growth for the growth of

crystals in supersaturated solution, m2

a activity of growing crystals (in Eq. (8.11))

a area of surface occupied by a molecule of vapor probe ( in Eq. (6.1))

a dimension of growth units normal to the step, m

B Langmuir constant, KL

b size of growth unit

Css moles of sucrose molecules on the crystal surface, molecules/m2.

c constant in BCF expression, m/s

c initial concentration and concentration of solute molecules at any time, t (in

Eq. (8.15))

c1 kinetic coefficient, m/s

ci, cs impurity concentration, g/L of water

co initial concentration solute molecules (in Eq. (8.15))

co solubility of sucrose at temperature T, molecules/m3

Deq equivalent diameter

Ds surface diffusion coefficient for solute molecules/atoms

d diameter of the crystal growth unit, m

d average distance between the adsorbed species, m

F constant in multiple nucleation model

Fmax maximal Feret diameter, m

xviii

Fmin minimal Feret diameter, m

fs area shape factor

fv volume shape factor

h height of elementary steps, m

hp planck’s constant, s-1

J rate of nucleation, nuclei/m2s

j James-Martin pressure drop correction factor

K overall growth kinetic constant, m/s

KL Langmuir constant, L/g

k Boltzmann constant

k1, k2 constant related to surface reaction constant and to the shape factors of

crystal

kd deactivation kinetic constant, s-1

′ik constant in Eq. (4.13)

L mean crystal size, m

La length of (110) face of sucrose crystal, m

Lagg average length agglomerated crystals, m

Lb length of (001) face of sucrose crystal, m

Lc length (100) face of sucrose crystal, m

Ll average length of largely accumulated crystals, m

Lm average length of medium agglomerated crystal, m

Lmono average length of monocrystals

Lo size of seed crystals

Ls average length of simple crystal, m

l average spacing between two adjacent adsorbed impurities, m

l average distance between dislocations

Mfinal mass of final crystals in the crystallizer, g

Minitial initial mass of crystals, g

m sample mass (in Eq. (6.2))

mo mass of seed crystals

xix

msucrose mass of seed crystals

N Avogadro number (in Eq. (6.1))

N number of growing crystals

N number of internal zones (in Chapter 7)

N overall growth kinetic exponent

No kink density

n1 concentration of monomers on the surface

nad number of adsorption sites occupied at a particular temperature

nmax maximum number of sites available for adsorption per unit area of a surface

no number of molecular positions available for adsorption on the crystal

surface

nso number of growth units per unit area of the surface

spn density of stable spirals in equilibrium

impuritysn , density of the adsorbed molecules in presence of impurity

puresn , density of the adsorbed molecules in pure solutions

p (= h/yo) spiral hillock of inclination

P perimeter (in Chapter 7)

Pi inlet pressure of the carrier gas

Po outlet pressure of the carrier gas

Qdiff differential heat of adsorption of the impurity on the surface

qd heat of adsorption, J/mol

qst isosteric heat of adsorption

R linear growth rate, m/s

Rg overall growth rate,

r2 coefficient of determination

rc critical radius of a stable circular nuclei

S supersatuation ratio

SSAsucrose specific surface area of the sucrose crystals

s measure of strength of the source of cooperating spirals

T column temperature

xx

Tr room temperature, K

Tw working temperature, K

t time, s

to dead time (mobile phase hold-up time), s

ts retention time of the probe liquids, s

VN net retention volume of probe molecule, s

VN,n-alkanes retention volume of n-alkanes, m3

VN,polar retention volume of the polar probe, m3

Vs mass of solvent inside the crystallizer, g

v frequency of atomic vibrations, s-1.

W activation energy for the integration of molecules/atoms, J/mol

w exit flow rate measured at 1atm and room temperature

Xagg fraction of agglomerated crystals

xo mean distance between two neighboring kinks of a spiral step, m

yo distance between consecutive turns of the spiral,

Greek letters

α impurity effectiveness factor introduced by Kubota and Mullin

β kinetic constant, m/s

1β dimensionless factor less than unity describing the influence of steps

1β height of an elementary step, h (SNM)

SNMβ constant in SNM model

γ surface free energy, J/m2

oγ surface free energy of pure sucrose crystal

DLγ dispersive liquid surface energy, mJ/m2

Dsγ dispersive solid surface energy, mJ/m2

edγ free edge work given by 2ded γγ = , J/m2

γp polar surface energy, mJ/m2

xxi

cG∆ Gibbs energy for the formation of stable nuclei

*G∆ Gibbs free energy corresponding to the formation of stable circular nuclei,

J/mol

speadsG∆ Gibbs specific surface energy, J/mol

oadsG∆ Gibbs free energy of adsorption, J/mol

DadsG∆ dispersive surface energy and specific, J/mol

dehG∆ Gibbs energy required for the dehydration of molecule/atom during its

integration into the crystal and the supersaturation, J/mol

hom2* DG∆ Gibbs free energy change required for the formation of stable two-

dimensional nuclei on a perfect surface, J/mol

H∆ enthalpy of impurity adsorption, J/mol

∆m change in the mass of crystals, g

S∆ entropy of impurity adsorption, J/mol

∆t time interval, s

θ fractional coverage of impurities on the adsorption sites

Λ dimensionless factor less than unity describing the influence of kinks in

steps

sλ average diffusion distance of the growth units on the surface, m

v frequency factor of the order of atomic vibration frequency

v average speed of surface adsorbed atoms/molecules, m/s

cρ density of the sucrose crystals, kg/m3

σ relative supersaturation (S-1)

υ averaged velocity of a step (arithmetic mean of oυ and minυ ), m/s

impυ ledge displacement rates in the occupied sites respectively, m/s

oυ ledge displacement rate, m/s

∞υ ledge velocity, m/s

Ω specific molecular volume of molecule or atom (m3)

mω surface area per adsorbed molecule, m2

xxii

Abbreviations

AN acceptor number, J/mol

DN donor number, Jmol-1

EPA electron pair acceptor

EPD electron pair donor

FID flame ionization

GRD growth rate dispersion

HAP hydroxyapatite

IGC inverse gas chromatography

INF influential factor

RPM revolutions per minute

SNM spiral nucleation model

SSA specific surface area

TCD thermal conductivity detector

xxiii

List of figuList of figuList of figuList of figuresresresres Fig. 2.1. Main groups of crystal faces: F- flat; S – stepped; K – Kinked. 10

Fig. 2.2. Spiral growth of crystals. 14

Fig. 2.3. Classification of crystal surface sites. 17

Fig. 2.4. Retardation of advancing steps due to adsorbed impurities in kink

sites according to Kubota-Mullin model.

19

Fig. 3.1. Batch crystallizer: R: Refractometer; s: seeds; A: agitator; t:

thermocouple.

24

Fig. 4.1a. Plot of linear growth rate versus supersaturation ratio for different

impurity concentrations at 30 oC.

30

Fig. 4.1b. Plot of linear growth rate versus supersaturation ratio for different


31

Fig. 4.2a. FTIR spectrum of Hodag CB6. 32

Fig. 4.2b. FTIR spectrum of pure sucrose. 32

Fig. 4.2c. FTIR spectrum of sucrose grown in solution with impurity (Hodag

CB6).

33

Fig. 4.3a. Experimental data and the birth spread kinetics for the growth of

sucrose crystals for different impurity concentrations at 30 oC.

35

Fig. 4.3b. Experimental data and the birth spread kinetics for the growth of

sucrose crystals for different impurity concentrations at 50 oC.

36

Fig. 4.4a. Plot of F and Ao versus impurity concentration, ci, for the growth

experiments at 30 oC.

37

Fig. 4.4b. Plot of F and Ao versus impurity concentration, ci, for the growth

experiments at 50 oC.

38

Fig. 4.5. Shishkovskii isotherm for Hodag CB6 onto sucrose particles. 41

Fig. 4.6. Surface coverage versus surfactant concentration at 30 and 50 ºC. 43

Fig. 4.7. Ratio of surface density of the adsorbed molecules versus impurity

concentration.

45

Fig. 4.8a. Experimental data and predicted BCF kinetics for the growth of 49

xxiv

sucrose crystals in pure and impure solutions at 30 oC.

Fig. 4.8b. Experimental data and predicted BCF kinetics for the growth of

sucrose crystals in pure and impure solutions at 50 oC.

50

Fig. 4.9a. Plot of σ1 and c versus impurity concentration at 30 oC. 51

Fig. 4.9b. Plot of σ1 and c versus impurity concentration at 50 oC. 52

Fig. 4.10. Effect of impurity concentration on the mean rate of advancement of

steps.

53

Fig. 5.1a. Experimental overall growth rate of sucrose crystals for different

surfactant concentrations at 30 oC.

62

Fig. 5.1b. Experimental overall growth rate of sucrose crystals for different

surfactant concentrations at 50 oC.

63

Fig. 5.2a. Effect of surfactant on the growth kinetics of sucrose crystals at 30 oC, according to SNM.

65

Fig. 5.2b. Effect of surfactant on the growth kinetics of sucrose crystals at 50 oC, according to SNM.

66

Fig. 5.3. Effect of surfactant concentration on the surface free energy,γ , at 30

and 50 oC.

67

Fig. 5.4. Plot of SNM kinetic constant, β SNM, versus surfactant concentration,

cs, at 30 and 50 oC.

68

Fig. 5.5. Shishkovskii’s plot for Hodag CB6 onto sucrose surfaces at 30 and 50 oC.

70

Fig. 6.1. Schematic diagram of the IGC experimental set-up used in this study

with head-space injections (For more details readers are suggested to check in

the manufactures website:

http://www.thesorptionsolution.com/Products_IGC.php).

82

Fig. 6.2. Experimental elution profiles of nonane, decane, undecane and

methane for the column packed with pure sucrose crystals at 50 oC.

83

Fig. 6.3a. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of n-alkanes onto

pure sucrose crystals.

88

Fig. 6.3b. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of n-alkanes onto 89

xxv

surfactant coated sucrose crystals.

Fig. 6.4a. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of polar probes

onto pure sucrose at 313.05 K.

91

Fig. 6.4b. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of polar probes

onto surfactant coated sucrose at 313.05 K.

92

Fig. 6.5a. Plot of ∆G/AN* versus DN/AN* for sorption of polar probes onto

pure and surfactant coated sucrose at 313.05 K.

93

Fig. 6.5b. Plot of ∆G/AN* versus DN/AN* for sorption of polar probes onto

pure and surfactant coated sucrose at 323.05 K.

94

Fig. 6.6. FTIR Spectrum of Hodag CB6. 95

Fig. 6.7. Plot of linear growth rate versus supersaturation ratio for different


98

Fig. 6.8. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of n-alkanes and

polar probes onto sucrose grown in the presence of impurities at 313.05 K.

99

Fig. 7.1. Classification of sucrose crystals according to its complexity. 108

Fig. 7.2a. Effect of impurity concentration on the influence factor for the

growth of sucrose crystals at 40 ºC.

111

Fig. 7.2b. Effect of impurity concentration on the length of simple and

agglomerated sucrose crystals (final crystal size) by image analysis.

112

Fig. 7.3. Three characteristic lengths of sucrose monocrystal lying on (100) or

( 001 ) crystallographic face.

114

Fig. 7.4a. Experimental and power law kinetics for the growth of (110) face of

sucrose crystal.

115

Fig. 7.4b. Experimental and power law kinetics for the growth of (001) face of

sucrose crystal.

116

Fig. 7.4c. Experimental and power law kinetics for the growth of (100) face of

sucrose crystal.

117

Fig. 7.5a. Multiple nucleation kinetics for the growth of (110) face of sucrose

crystals at 40 oC.

119

xxvi

Fig. 7.5b. Multiple nucleation kinetics for the growth of (001) face of sucrose

crystals at 40 oC.

120

Fig. 7.5c. Multiple nucleation kinetics for the growth of (100) face of sucrose

crystals at 40 oC.

121

Fig. 7.6. Shiskovskii isotherm for the sorption of Hodag CB6 onto sucrose

surface at 40 oC.

126

Fig. 7.7a. Experimental data and BCF kinetics for the growth of (110) face of

sucrose crystal at different impurity concentrations.

129

Fig. 7.7b. Experimental data and BCF kinetics for the growth of (001) face of


130

Fig. 7.7c. Experimental data and BCF kinetics for the growth of (100) face of


131

Fig. 8.1. Concentration profile during the growth of sucrose crystals at 313 K. 143

Fig. 8.2a. Plot of

−−

− ∞

cc

cc

A s

sln1

ln versus time, t, for the growth of

sucrose crystals for different agitation speeds at 313 K.

145

Fig. 8.2b. Plot of lnAcccc ss

111

−−

− ∞

versus time, t, for the growth of

sucrose crystals for different agitation speeds at 313 K.

145

Fig. 8.3. Plot of lnAcccc ss

111

−−

− ∞

versus time, t, for the growth of

sucrose crystals at 303 and 313 K.

147

xxvii

List of tablesList of tablesList of tablesList of tables

Table 4.1. Fitted kinetic parameters according a power law growth kinetics. 33

Table 4.2. Thermodynamic parameters for the sorption of surfactant onto

sucrose surface.

44

Table 4.3. Kinetic constant and activation energy by multiple nucleation

model.

46

Table 4.4. Energy of adsorption for the sorption of sucrose molecules onto the

crystal surface determined by BCF theory.

48

Table 5.1. Activation energy for sucrose growth according to SNM. 72

Table 6.1. Characteristics of the probes used in this study (Gutmann, 1978;

Drago and Wayland, 1977; Yang et al., 2008; Flour and Papirer, 1983; Riddle

and Fowkes, 1990; Lavielle et al., 1991; Schultz et al., 1987; Dong et al.,

1989).

87

Table 6.2. γsD, sp

adsG∆ , KA and KB for polar and n-alkanes onto pure and

surfactant coated sucrose particles at 313.05 and 323.05 K.

92

Table 6.3. Enthalpy and isosteric heat of adsorption for the sorption of polar

probes onto pure and surfactant coated sucrose particles at 313.05 and 323.05

K.

97

Table 6.4. γsD and sp

adsG∆ for polar and n-alkanes onto sucrose crystals grown in

the presence of different surfactant concentration.

100

Table 7.1. Experimental conditions and number of crystals analyzed to study

the agglomeration effect of Hodag CB6 on the final crystals.

110

Table 7.2. Kinetic constant and order of reaction of power law expression for

the growing faces (110, 001, 100) of sucrose crystals.

115

Table 7.3. Kinetic and thermodynamic parameters determined from multiple

nucleation model.

119

Table 7.4. Kinetic constant, surface free energy and energy of activation for the

growth of crystals for pure and impure system by multiple nucleation model

125

xxviii

during the growth of (110), (001), and (100) faces of sucrose crystals.

Table 7.5. Langmuir constant, KL, values and differential heat of adsorption of

the impurity on the surface, Qdiff, for the three growing faces of sucrose

crystals.

126

Table 7.6. Kinetic and thermodynamic parameter in the BCF equation for the

growth of (110), (001), (100) crystal faces of sucrose at 40 oC.

131

Table 8.1. Determined kinetic coefficient and the corresponding coefficient of

determination by Eq. (8.21) and (8.25) for the growth of sucrose crystals in

pure solutions.

144

Chapter 1Chapter 1Chapter 1Chapter 1

Growth of crystals in impure solutionGrowth of crystals in impure solutionGrowth of crystals in impure solutionGrowth of crystals in impure solution:::: An introductionAn introductionAn introductionAn introduction

Abstract

The works presented in the thesis are explained in brief in this chapter. It starts with an

introduction explaining the background of crystal growth process in pure and impure

solutions. Later the main objectives of this research work and the work plan have been

explained including a crisp survey on similar works available in literatures. This chapter

finally ends with an overview of the remaining chapters of the thesis.

1.1.1.1.1. 1. 1. 1. CrystaCrystaCrystaCrystallizationllizationllizationllization

Crystallization is an important operation in processing as a method of both purification

and of providing crystalline in desired size range. Growth of crystals in solutions is

usually modeled using the kinetic data. The mechanisms behind the crystal growth

process are usually modeled either from kinetic experimental data obtained by growing

single crystals or from the growth of a suspension of crystals in solution under controlled

conditions. The controlled conditions refer to the seeded growth process without allowing

nucleation to occur. For a crystal growing in solution in the absence of any foreign

particles, it was observed that all the faces grow at a constant rate and the crystals

develop in a regular manner.

Several studies showed that the presence of impurities in solution will

significantly interfere with the growth rate of crystals, morphology of the crystals and

also with the agglomeration rate. The kinetics of crystal growth from aqueous solution is

a very complex process, because of the multiple steps (diffusion and integration)

involved. The presence of impurity may play a significant role in either of these steps

(Sangwal, 1999). The presence of impurities also showed a significant alteration in the

morphology of the growing crystals (Murugakoothan et al., 1999; Sangwal, 1996;

Sangwal, 1993). Several works have been reported dealing with the effect of impurities

on the growth and dissolution kinetics of crystals in solutions (Murugakoothan et al.,

1999; Sangwal, 1996; Sangwal, 1993; Sangwal, 1999; Kuznetskov et al., 1998; Sangwal

2

and Mielniczek-Brzóska, 2001a; Kubota et al., 2001; Sangwal and Brzóska, 2001b). The

impurities either increase or decrease the growth rate of crystals depending on the surface

properties of the crystal, impurity and also on the solute. Some impurities may exhibit

selective influence on a particular crystallographic face (Sgualdino et al., 2006;

Sgualdino et al., 2000; Sgualdino et al., 1998; Murugakoothan et al., 1999).

The impurities intensively added to either alter the growth rate of growing crystals

or to modify the crystallographic structure are in general called as additives. The effects

of additives can be classified as thermodynamic effects or kinetic effects (Jibbouri et al.,

2002). Many investigations are being carried out to explain the effect of impurity on the

growth kinetics for several crystallization systems (Jibbouri et al., 2002; Sgualdino et al.,

2006; Martins et al., 2006). Most of the literature reports the inhibiting effect of impurity

on the crystal growth kinetics. The inhibiting effect of additives was explained based on

the adsorption of impurity in the kink sites. Growth promoting effect of impurity was

explained for few crystallization systems. The growth promoting effect was found to be

influenced by the concentration of additives.

The inhibiting effects of additive or impurity on the growth of crystals are usually

modeled based on the mechanism of impurity sorption in kinks and in terrace considering

the kinetic effects (Jibbouri et al., 2002). The increase in growth rate was usually

modeled considering the thermodynamic effect which is due to the adsorption of impurity

on growing surface leading to decrease in the surface energy (Davey, 1976; Sangwal and

Brzóska, 2001 & 2000b; Kuznetskov et al., 1998). Many investigations are carried out

mainly focusing on the kinetics effects of impurities. Only few studies are dedicated

towards the thermodynamic effects due to the addition of impurities.

1.2. Motivation and Objectives

Several kinetic models were used to explain the kinetics and thermodynamic effects of

the impurities on the crystal growth process. Kubota-Mullin (Kubota, 2001) and Cabrera-

Vermilyea (1958) models are the most widely used kinetics to explain the inhibiting

effect of the impurities on the crystal growth process. Recently the kinetic effect of added

impurity was proposed and explained based on a competitive sorption model for the

growth of sucrose crystals (Martins et al., 2006). BCF surface diffusion model (Burton et

al., 1951), multiple nucleation model (Sangwal, 2008) and a model involving the

3

complex source of cooperating dislocations (Sangwal, 2008) were found to be excellent

in explaining the kinetic and thermodynamic effects simultaneously.

The aim of the present study is to model the growth promoting effect of the added

impurity at different solution temperatures using several kinetic models. In the present

study, a simple linear form of spiral nucleation model was also presented to explain the

kinetics and thermodynamic effect simultaneously of the added impurity on the growth

kinetics. The experimental growth kinetics is also modeled using the classical BCF

surface diffusion and multiple nucleation models. The determined kinetic parameters

were also used to study and understand the effect of interfacial tension on the topological

parameters.

In addition to the kinetic models, the effect of the added surfactant, Hodag CB6,

on the surface properties of the sucrose crystal and on the surface free energy was studied

in detail by Inverse Gas Chromatography (IGC) technique. Two types of samples, the

sucrose coated with surfactant and the sucrose from the crystal growth experiments in

presence of surfactant were analyzed using IGC. Retention time of polar and apolar

probes were employed to determine the effect of emulsifier on the dispersive surface

energy, acid-base parameters and adsorption thermodynamics.

The effect of the Hodag CB6 on the surface morphology and on the

agglomeration degree of the sucrose crystals during the growth process was studied using

the well established image analysis technique. In addition, in the present research, the

well established image analysis was used to study the mean face growth rate of the

sucrose crystals as a function of impurity concentration. The mean face growth rates were

monitored using an offline image analysis technique. The determined mean face growth

rates were used to study the kinetic and thermodynamic effect of Hodag CB6 on the

mean growth rate of (110), (001) and (100) faces of sucrose crystals as a function of

impurity concentration. Further, the offline image analysis technique was used to predict

the kinetic and thermodynamic effect of added impurity on the growing crystals in a

batch crystallizer.

In a batch crystallization process, it is obvious that the supersaturation changes

with the growth of crystals during the growth process which in turn will influence the

activity of dislocations on the crystal surface. It is believed and accepted by several

4

researchers about the GRD during the growth of crystals due to the activity of

dislocations on the crystal surface (Burton et al., 1951; Shiau, 2003; Randolph and White,

1977; Berglund, 1980; Berglund and Murphy, 1986; Garside et al., 1976; Lacmann et al.,

1999). However, to the best of the knowledge is concerned, no studies have been reported

explaining the rate of change in activity of dislocation spirals, which is expected during a

course of time in a batch crystal growth process. Thus, the deactivation kinetics of

dislocation activity, which is expected due to the change in supersaturation that decreases

with reaction time, irrespective of the limiting step (diffusion or surface reaction) during

a batch crystallization process, was studied using the sucrose crystals growth

experiments. Kinetic models are proposed to explain the kinetics of change in dislocation

activities on the crystal surfaces for the limiting conditions of surface diffusion or surface

integration. The proposed kinetic model was used to explain the rate of change in

activities on the surface of sucrose crystals (collective) during the growth process in pure

solutions.

1.3. Structure of the thesis

The results explaining the accomplished objectives are presented in the rest of the

chapters of this thesis. Chapter 2 gives a description of the theoretical models that are

used in the thesis to explain and identify the crystal growth mechanism in pure and

impure solutions. Chapter 3 describes the experimental set up of the batch crystallizer

that we used for growing the crystals in pure and impure solutions. In this chapter, some

of the important details of the sucrose crystals and the non-ionic surfactant, Hodag CB6,

which are used in the experiments, are also presented.

Chapters 4 to 8 explain the main results and discussion of these results of the

present investigation. Much attention was made to construct these chapters in a way that

allows them to be read individually. Experimental section was included in all of these

chapters in addition to that explained in Chapter 3, to make these chapters stand alone by

themselves.

In Chapter 4, the effect of impurity (surfactant) on the growth of sucrose crystals

was analyzed in the light of well established crystal growth kinetic models: surface

diffusion model and a multiple nucleation model. In Chapter 5, the effect of the added

surfactant was analyzed using a model (Spiral Nucleation Model) proposed by this

5

research group in recent years. In both of these chapters the determined kinetic and

thermodynamic parameters were used to estimate the morphological parameters of the

growing crystals in solution.

Chapter 6, explains the applicability of Inverse Gas Chromatography (IGC) in

estimating the surface properties of sucrose crystals grown in pure and impure solutions.

Further, this chapter also presents the effect of surfactant coated on the surface of the

sucrose crystals, analyzed using the IGC technique.

In Chapter 7, the kinetic and thermodynamic effect of Hodag CB6 on the mean

growth rate of (110), (001) and (100) faces of sucrose crystals were analyzed using an

offline image analysis technique. The growth promoting effect of the added surfactant on

the face growth rate of crystals was studied and explained in this chapter based on surface

diffusion and multiple nucleation models. The effect of impurity on the agglomeration

degree of the crystals was studied and reported in this chapter based on the morphological

parameters obtained by the offline image analysis technique.

Under Chapter 8, new kinetic models based on the concepts of Burton-Cabrera-

Frank (BCF) theory are proposed to explain the change in activity of dislocation spirals

on the surfaces of crystal collective during a crystal growth process in diffusion and in

kinetic regime. The applicability of the proposed models to the experimental crystal

growth kinetics of sucrose in pure solutions and the advantages of these models were

explained in detail in this chapter.

Finally in Chapter 9, the contributions of the present research and few suggestions

for future work are made.

6

1.4. References

Al-Jibbouri, S., Strege, C. and Ulrich, J. (2002). Crystallization kinetics of epsomite

influenced by pH-value and impurities. J. Cryst. Growth. 236, 400-406.

Berglund, K.A. (1980). Growth and size distribution kinetics for sucrose crystals in the

sucrose-water system, M.S. Thesis, Colorado State University, Ft. Collins, 1980.

Berglund, K.A. and Murphy, V.G. (1986). Modeling growth rate dispersion in a batch

sucrose crystallizer. Ind. Eng. Chem. Fundam. 25, 174-176

Burton, W.K., Cabrera, N. and Frank, F.C. (1951). The growth of crystals and the

equilibrium structure of their surfaces. Philos. Trans. R. Soc. A. 1934, 299-358.

Cabrera, N. and Vermilyea, D.A. in: R.H. Domeus, B.W.Roberts, D. Turnbull (Eds.),

(1958). Growth and perfection of crystals, Wiley, New York, p.393.

Davey, R.J. (1976). The effect of impurity adsorption on the kinetics of crystal growth

from solution. J. Cryst. Growth. 34, 109-119.

Garside, J., Philips, V.R. and Shah, M.B. (1976). On size-dependent crystal growth, Ind.

Eng. Chem. Fundam. 15(3), 230-233.

Kubota, N. (2001). Effect of impurities on the growth kinetics of crystals., Cryst. Res.

Technol. 36, 8-10.

Kubota, N., Yokota, M. and Mullin, J. W.(2000). The combined influence of

supersaturation and impurity concentration on crystal growth. J. Cryst. Growth.

212, 480-488.

Kuznetsov, V.A., Okhrimenko, T.M. and Rak, M. (1998). Growth promoting effect of

organic impurities on growth kinetics of KAP and KDP crystals. J. Cryst. Growth.

193, 164-173.

Lacmann, R., Herden, A. and Chr. Mayer. (1999). Kinetics of nucleation and crystal

growth., Chem. Eng. Technol. 22, 279-289.

Martins, P.M., Rocha, F. and Rein, P. (2006). The influence on the crystal growth

kinetics according to a competitive adsorption model. Cryst. Growth. Des. 6(12),

2814-2821.

Murugakoothan, P., Kumar, R.M., Ushasree, P.M., Jayavel, R., Dhanasekaran, R. and

Ramasamy, P. (1999). Habit modification of potassium acid phthalate (KAP) single

crystals by impurities. J. Cryst. Growth. 207, 325-329

7

Randolph, A.D. and White, E.T. (1977). Modeling size dispersion in the prediction of

crystal-size distribution, Chem. Eng. Sci. 32, 1067-1076.

Sangwal, K. (1993). Effect of impurities on the processes of crystal growth. J. Cryst.

Growth. 128, 1236-1244.

Sangwal, K. (1996). Effects of impurities on crystal growth processes. Prog. Cryst.

Growth Charact. Mater. 32, 3-43.

Sangwal , K. (1999). Kinetic effects of impurities on the growth of single crystals from

solutions. J. Cryst. Growth. 203, 197-212.

Sangwal, K. (2008). Additives and crystallization processes: From fundamentals to

applications, John Wiley & Sons, Ltd.

Sangwal, K. and Brzóska, E.M. (2001a). Effect of Fe(III) ions on the growth kinetics of

ammonium oxalate monohydrate crystals from aqueous solutions. J. Cryst. Growth.

233, 343-354

Sangwal, K. and Brzóska, E.M. (2001b). On the effect of Cu(II) impurity on the growth

kinetics of ammonium oxalate monohydrate crystals from aqueous solutions. Cryst.

Res. Technol. 36, 837-849.

Sgualdino, G., Aquilano, D., Cincotti, A., Pastero, L. and Vaccari, G. (2006). Face-by-

face growth of sucrose crystals from aqueous solutions in the presence of raffinose.

I. Experiments and kinetic-adsorption model. J. Cryst. Growth. 292, 92-103.

Sgualdino, G., Aquilano, D., Tamburini, E., Vaccari, G. and Mantovani, G. (2000). On

the relations between morphological and structural modifications in sucrose crystals

grown in the presence of tailor-made additives: effects of mono- and

oligosaccharides.Mat Chem Phys. 66, 316-322.

Sgualdino, G., Aquilano, D., Vaccari, G., Mantovani, G. and Salamone, A. (1998).

Growth morphology of sucrose crystals: The role of glucose and fructose as habit-

modifiers. J. Cryst. Growth. 192, 290-299.

Shiau, L.-D. (2003). The distribution of dislocation activities among crystals in sucrose

crystallization. Chem. Eng. Sci. 58, 5299-5304.

Chapter Chapter Chapter Chapter 2222

Effect of Effect of Effect of Effect of Impurities on Crystal Growth Kinetics: TheoriesImpurities on Crystal Growth Kinetics: TheoriesImpurities on Crystal Growth Kinetics: TheoriesImpurities on Crystal Growth Kinetics: Theories

Abstract

Studies on the effect of impurities on the crystal growth process began early in 1950’s

and 1960’s by Frank (1958), Bliznakov (1954, 1958, 1965), Bliznakov and Kirkova

(1957, 1969), Bienfait et al. (1965) and by Kern (1967). Cabrera and Vermilyea (1958)

theoretically explained the growth inhibiting effect of impurities based on the adsorption

of impurity molecules on surface terrace in the motion of ledges across the surface.

Dunning and Albon (1958), and Dunning et al (1965) proposed the model of adsorption

of impurity molecules at ledges of a face and tested the validity of their model against the

background of the dependence of rate of motion of growth layers on impurity

concentration. Bliznakov (1954, 1958, 1965) introduced the kinetic model explaining the

growth inhibiting effect of impurities based on the adsorption of impurities on the active

growth sites of growing faces. Later Chernov (1961, 1984) explained the adsorption of

impurities on kink position in a ledge and put forwarded the concepts of adsorption of

impurities in kinks after Bliznakov. Until 1970’s, most of the works explaining the

influence of impurities on the crystal growth process are focused on the kinetic effect of

impurities, and the thermodynamic effect of impurities is least studied.

In 1976, Davey introduced the concepts of kinetic and thermodynamic effect of

impurities. The concepts of Davey (1976) lead a path to several researchers to study the

kinetic and thermodynamic effect of impurites, mainly to explain the growth promoting

effect of impurities in a growth process. Recently Kubota and Mullin (1995) advanced a

new kinetic model of growth in the presence of impurities. The model describes the

adsorption of an impurity along steps and introduces an effectiveness parameter α for the

impurity adsorption. More recently, a competitive sorption model was proposed by

Martins and Rocha (2006), considering the competitive effect of impurities with the

solute molecules. This model introduces a new parameter β in addition to α

corresponding to the competition effect of impurity molecules within the solute particles

and the kinetic effect of impurity during the growth process.

10

Any foreign compounds other than the crystallizing compound in the suspension

are considered as an impurity. The impurities either increase or decrease the growth rate

of crystals depending on the surface properties of the crystal, impurity and also on the

solute. Some impurities may exhibit selective influence on a particular crystallographic

face. The impurities intensively added to either alter the growth rate of growing crystals

or to modify the crystallographic structure are in general called as additives. The

inhibiting effect of additives could be explained based on the adsorption of impurity in

the kink sites, steps and terraces (crystal side). The increase in growth rate could be

modeled considering the thermodynamic effect which is due to the decrease in surface

energy due to adsorption of impurity on growing surface.

2.1. Growth Models

The growth of crystals in pure and impure solutions may be flat (F), stepped (S) and

kinks (K). Crystals of visible size are usually bounded by the slowly-growing F faces

which grow by the attachment of growth units at energetically favorable sites.

Fig. 2.1. Main groups of crystal faces: F- flat; S – stepped; K – Kinked.

11

Fig. 2.1 shows different positions for the attachment of growth units at a flat

crystal-medium interface of a simple cubic lattice. Impurities contained in a growth

medium affect the kinetics of growth of all types of faces of a crystal. According to the

concepts of Hartman (1973, 1987), F faces are smooth on a molecular level and contain

low density of kinks, while S and K faces are rough and contain a relatively higher

density of kinks. Thus the growth of F faces is possible only when growth layers emitted

by dislocation emerging on the surface or two-dimensional nuclei forming on it provide

kinks necessary for the attachment of growth units. The S and K faces contain roughness

and thus it does not require the presence of dislocation or two-dimensional nucleation for

growth.

2.1.1. Layer growth of F faces

Growth of perfect faces devoid of dislocation is possible by incorporation of growth units

at the kinks of steps supplied by two-dimensional nucleation (2D nucleation). A single

dislocation on a perfect crystal devoid of dislocation bound more weakly than an adatom

in a cluster of adatoms on the surface. Thus an energy barrier to the formation of new

crystal layer is required. This situation is the 2D analogue of homogenous nucleation and

hence the rate of growth of this face will be determined by the frequency of formation of

2D nuclei. Depending on the rate of displacement of steps of the nuclei, v, three versions

of growth by 2D nucleation have been proposed namely mononuclear, polynuclear and

Birth and Spread or multiple nucleation model.

2.1.1.1. Mononuclear model

Mononuclear model physically reflects the birth of critical size nucleus on a flat surface

and then this nucleus spreads across the surface at an infinite velocity followed by an

intermission before the next critical size nucleus appears. If A represents the total surface

area on a crystal surface, then AJ represents the new nuclei formed per unit time. But

each nucleus results in growth perpendicular to the surface of an amount h (Ohara and

Reid, 1973). Thus the growth rate is simply

hAJR = (2.1)

The rate of nucleation, J is given by

∆−=kT

GCJ

*2/1

1 expσ (2.2)

12

where

2/1211

2

Ω

=h

DnC sπ (2.3)

The free energy corresponding to the formation of stable circular nuclei of a critical

radius, rc, on the perfect surface is

σγπ

kT

hG

Ω=∆2

* (2.4)

2.1.1.2. Polynuclear model

This model is based on assumption that the born critical size nucleus does not spread, i.e.,

υ = 0. Thus the crystals growth is due to the accumulation of sufficient number of

critical nuclei to cover the entire surface. Thus for a unit area of surface, the volume of

new material deposited per unit time is ( )hrJ c2π ; this also represents the net growth rate

perpendicular to flat surface (Ohara and Reid, 1973)

hJrR c2π= (2.5)

where rc is given by

( )SkTrc ln

Ω= γ (2.6)

2.1.1.3. Birth and Spread model

Birth and spread model allows both nucleation of critical size embryos and subsequent

growth at a finite rate. The important assumption of this model regarding the growth or

spread of the nuclei are (a) there is no intergrowth between nuclei, i.e., the nuclei can slip

over the surface, (b) the lateral spreading velocity is a constant and independent of the

island size and (c) nuclei can born anywhere on incomplete layer as well as on islands.

The two-dimensional nucleation rate, J, ledge velocity, ∞υ and the face growth rate R are

given by (Ohara and Reid, 1973; Sangwal, 1994; Sangwal, 1996)

Ω−

Ω

=σ

γπσπ 22

22/1

2/121 exp

2

Tk

h

hvnJ (2.7)

s

sos

h

nD

λσβυ ΛΩ

=∞2

(2.8)

and

13

Ω−

Λ== ∞ σ

γπσλ

βυ22

26/5

3/2

3/23/1

3exp'

Tk

h

v

nDAhJR

s

sos (2.9)

where A’ is a constant, Ds is the surface diffusion coefficient for solute molecules/atoms

adsorbed on the surface, n1 is the concentration of monomers on the surface and

( ) 2/118 mkTv π= is the average speed of surface adsorbed atoms/molecules (m is their

mass).

According to Eq. (2.9), growth rates of faces having a high density of kinks (i.e., at high

supersaturations) may be expressed as (Sangwal, 1996)

6/5

3/2

' σλ

β

Λ=

v

NDAR

s

os (2.10)

Thus at high supersaturation, R increases more or less linearly with supersaturation.

2.1.2. Two dimensional nucleation models with surface diffusion and two

dimensional models with direct integration

The rate expressions of polynuclear and multiple nucleation models based on the surface

diffusion and direct integration are essentially the same. The difference between the

equations of R based on surface diffusion and direct integration of growth units lies in the

expressions of v and J in the two cases.

In the case of direct integration (Malkin et al., 1989), υ and J are given by

σβυ 1ocΩ= (2.11)

( )kTGCJ /exp *2/12 ∆−= σ (2.12)

Where the constant, C2 is given by

112 βπ ochnC = (2.13)

And β1 is a kinetic coefficient, given by

( )kTWbv /exp1 −=β (2.14)

where, W is the activation energy for the integration of molecules/atoms into the kink. It

should be noted that in the step kinetic coefficient, b is the size of growth unit, and υ is

the frequency of atomic vibrations, s-1.

Substituting Eq. (2.11) to (2.14) in Eq. (2.9), we get

14

( )

∆−Ω=

kT

GCchR o 3

exp*

6/53/12

3/23/2 σβ (2.15)

The forms of multiple nucleation model based on surface diffusion and direct integration

are essentially the same. Likewise the polynuclear model for surface diffusion and direct

integration could be derived easily which is essentially the same as in the case of multiple

nucleation model (Sangwal, 1996).

2.1.3. Spiral growth models

If the F crystal face is not perfect and in particular if screw dislocations are present, then

these screw dislocations represent a non-vanishing source of steps which alleviate the

necessity of a 2D nucleation growth mechanism. Instead the growth rate is determined by

the rate of the lateral movement of the steps. This is the case of S and K faces where the

surfaces are endowed with a high density of kinks on them. If an array of steps of height,

h, and interstep distance, yo, forming a spiral hillock of inclination, p = h/yo, traverses

across a growing surface at a rate, υ , then the normal growth rate is given by (Fig. 2.2)

υυp

y

hR

o

== (2.16)

Fig. 2.2. Spiral growth of crystals.

15

where the interstep distance yo is related with the radius rc of the critically sized circular

nucleus corresponding to activation barrier *pG∆ by

σγ

kTry co

Ω== 1919 (2.17)

The hillock inclination p is a constant and the supersaturation available on the surface is

equal to the bulk supersaturation in the solution.

Burton, Cabrera and Frank (BCF) developed the theory of screw dislocation crystal

growth and found that the step velocity and the face growth rate R are given by

Λ

=s

os y

b λββλσυ

2tanh2 *

1 (2.18)

and

=

σσ

σσ 1

1

2* tanhCR (2.19)

where

ββb

NC oΛΩ

=*1* (2.20)

and

skTλγσ

2

191

Ω= (2.21)

where No is the concentration of growth units on the surface. The kinetic coefficient, β is

given by

∆−=

kT

Gbv dehexpβ (2.22)

dehG∆ is the energy required for the dehydration of molecule/atom during its integration

into the crystal.

At lower supersaturaitons, σσ >>1 , so ( )σσ /tanh c 1, hence

=

1

2*

σσ

CR (2.23)

Eq. (2.23) is the BCF parabolic law.

16

At supersaturation sufficiently higher than 1σ , tanh(x0)=x, thus

σ*CR = (2.24)

In this model, the kink retardation factor, *1β , describes the influence of kinks in steps

while the step retardation factor,Λ , that of the density of steps. Their values depend on

σ but their relationship with σ is complicated. In general, υ depends on σ through β,

Λ and yo at low σ while only through β and Λ at high σ (Sangwal, 1996).

According to the direct integration model (Chernov, 1961; Chernov et al., 1986), the step

velocity υ is given by Eq. (2.11) while the face growth rate is given by

2σCR = (2.25)

where the constant C is given by

γβ

191okThc

C = (2.26)

where 1β is given by Eq. (2.14).

The structures of Eq. (2.25) and Eq. (2.19) are essentially the same at low σ when

σ << 1σ and ( ) 1tanh 1 =σσ .

2.1.4. Spiral nucleation model

This model combines the concepts of 2D nucleation and BCF model to explain the

growth kinetics of sucrose crystals. The transient kinetic behaviour of the growth process

according to SNM is given by (Martins and Rocha, 2007):

σβπρ1

2

exp2

−=kT

Wvn

y

h

L

Rsp

o

g (2.27)

where the term,1β , is a constant and is equal to the height of an elementary step, h.

The density of stable spirals in equilibrium is given by (Martins and Rocha, 2007):

∆−=

kT

G

l

yn co

sp exp2

λ (2.28)

From Eqs. (2.27) and (2.28), it could be realized that this model incorporates the Gibbs

free energy corresponding to the energy barrier required for nucleation and the activation

energy corresponding to step growth kinetics.

17

2.1.5. Adsorption of impurities on F faces: Kinetic models

Adsorption of impurity on a F face affects the thermodynamic and kinetic terms involved

in growth model and also affects the solubility for higher impurity concentrations. Davey

(1974) showed that the adsorption of impurity decreases the value of surface energy, γ,

due to the adsorption of impurities. This decrease in γ will consequently cause an increase

in growth rate. The kinetic term in growth theories is directly related to the velocity of

movement of steps, ∞υ , on the crystal surface. Impurities adsorbed on the surface

decrease the velocity of movement of steps by decreasing the values of kink retardation

factor, β and the step retardation factor, Λ . The coverage of impurities on the adsorption

sites can be explained using the parameter θ , which is defined by

max/ nnad=θ (2.29)

where nmax is the maximum number of sites available for adsorption per unit area of a

surface for a given growth conditions and nad is the number of adsorption sites occupied

at a particular temperature. When all the sites are occupied, 1=θ .

Fig. 2.3. Classification of crystal surface sites.

18

According to Bliznakov (1954, 1958, 1965), the movement of a growth ledge is

influenced by the adsorption of impurities in kink positions and the effective

displacement rate of ledge is given by

( ) θυθυυ impo +−= 1 (2.30)

where, oυ and impυ represent the ledge displacement rates in the unoccupied and

occupied sites respectively. The coverage of adsorption sites θ can be described by

adsorption isotherms like Freundlich, Langmuir and Temkin isotherms (Davey and

Mullin, 1974; Oscik, 1982).

2.1.5.1. Cabrera and Vermilyea model (1958)

When the impurity strongly adsorbs on a surface rather than ledges and the adsorbed

particles are immobile when compared to the mobility of ledges, then according to

Cabrera and Vermilyea (1958), the velocity of a straight step, oυ and the velocity, ρυ of a

step of curvature ρ are related by

ρρ

υυρ c

o

−= 1 (2.31)

From the definition of fractional coverage of adsorption sites by impurity molecules per

unit area, the average distance between the adsorbed species may be expressed as

( ) 2/1max2 −== θρ nd (2.32)

When the advancing ledge contacts an impurity particle, it tends to curl around this

particle. The step will stop when d < 2cρ , while it squeezes between a pair of

neighboring impurity particles when d > 2cρ . Thus the velocity of the movement of

straight ledges will be modified and the average velocity will be smaller thanoυ .

Assuming the mean velocity of the step, ( ) 2/1ρυυυ o= , the mean velocity can be written

as

( ) ( ) 2/1max

2/1 21/21 θρυρυυ nd coco −=−= (2.33)

2.1.5.2. Kubota-Mullin model (1995)

Recently Kubota and Mullin (1995) proposed a new model based on Cabrera and

Vermilyea (1958) model assuming that the advancement of steps are hindered by

impurity species adsorbing on the step lines in the kink sites. This model further assumes

19

that the step displacement is pinned by impurities at the points of their adsorption and the

step is forced to curve as shown in Fig. 2.4.

Fig. 2.4. Retardation of advancing steps due to adsorbed impurities in kink sites according to Kubota-Mullin model.

According to this model the time averaged velocity υ of a step is approximated by the

arithmetic mean of oυ and minυ as

( )2

minυυυ += o (2.34)

where, minυ refers to the instantaneous minimum step velocity given at a curvature of

2/l=ρ (l is the average spacing between two adjacent adsorbed impurities).

From Eq. (2.31) and Eq. (2.34), the average advancement velocity can be written as

lc

o

ρυυ −= 1 (2.35)

The coverage of active sites by impurities can be related to the average distance between

the active sites, d, from a simple geometric consideration, under the assumption of linear

adsorption on the step lines as

l

d=θ (2.36)

The critical radius of a two-dimensional nucleus is given by Burton et al. (1951) as

σγρ

kT

ac = (2.37)

where a in Eq. (2.37) refers to the size of a growth unit.

Crystal

Impurities

Step

20

Substituting Eqs. (2.36) and (2.37), the Kubota-Mullin model is given by

αθθσ

γυυ −=

−= 11dkT

a

o

(2.38)

where, α is the impurity effectiveness factor introduced by Kubota and Mullin explaining

the activity of the added impurities on the growth process.

2.1.5.3. Competitive sorption model (Martins et al., 2006)

Recently a mathematical model describing the growth of crystals in impure solution was

proposed assuming the competitive sorption of solute molecules and impurities

11

++−=

kSck

ck

R

R

ii

ii

o

β (2.39)

The term β reflects the tendency of impurity molecules to replace the crystallizing solute

in the active sites during the growth process. For β > 1 the fraction of active sites

occupied by the impurity is higher than the surface coverage. For β < 1, the crystal

growth process can be slowed by the presence of impurities.

In this study, since the added surfactant showed a growth promoting effect for the

sucrose crystals in solutions at the studied experimental conditions, only the multiple

nucleation, BCF surface diffusion and spiral nucleation models were taken under

consideration. These models have the advantages to explain the kinetic and

thermodynamic effect simultaneously.

21

2.2. References

Bienfait, M., Boistelle, R. and Kern, R. (1965). In: Adsorption et Croissance Cristalline

(R. Kern, ed.), p. 557. CNRS, Paris. †

Bliznakov, G.M. (1954). Bull. Acs. Sci. Bulg. Ser. Phy. 4, 135. †

Bliznakov, G.M. (1958). Fortschr. Min. 36, 149. †

Bliznakov, G.M. (1965). In: Adsorption et Croissance Cristalline (R. Kern, ed.), p. 291.

CNRS, Paris. †

Bliznakov, G.M. and Kirkova, E.K. (1957). Z. Phys. Chem. 206, 271. †

Bliznakov, G.M. and Kirkova, E.K. (1969). Krist. Tech. 4, 331. †

Burton, W.K., Cabrera, N. Frank, F.C. (1951). The growth of crystals and the equilibrium

structure of their surfaces. Phil. Trans. R. Soc. Lond. A. 12, 299-358.

Cabrera, N. and Vermilyea, D.A. (1958). In: Growth and Perfection of Crystals (R.H.

Doremus, B.W. Roberts and D. Turnbull, eds.), p. 393, Wiley, New York. †

Chernov, A.A. (1961). Uspekhi Fiz. Nauk 73, 277-331. English Translation.: The spiral

growth of crystals, Sov. Phys.Uspekhi 4(1), 116-148.

Chernov, A.A. (1984). Modern Crystallography III: Crystal Growth. Springer, Berlin.

Chernov, A.A., Rashkovich, L.N., Smolski, I.L. Yu, G. and Kuznetsov, A., Mkrtchyan,

A. and Malkin, A.I. (1986). Rost Kristallov, 15, 43. †


from solution. J. Cryst. Growth 34, 109-119.

Davey, R.J., Mullin, J.W. (1974). Growth of the 100 faces of ammonium dihydrogen

phosphate crystals in the presence of ionic species. J. Cryst. Growth 26,45-51.

Dunning, W.J. and Albon, N. (1958). In: Growth and Perfection of Crystals (R.H.

Domeus, B.W. Roberts and Turnbull, D. eds.), p. 411. Wiley, New York. †

Dunning, W.J., Kackson, R.W. and Mead, D.G. (1965). In: Adsorption et Croissance

Cristalline (R. Kern, ed.), p. 303. CNRS, Paris. †

Frank, F.C. (1958). In: Growth and Perfection of Crystals (R.H. Doremus, B.W. Roberts

and D. Turnbull, eds.), p. 411. Wiley, New York.†

Hartman, P. (1973). In: Crystal Growth: an Introduction (P. Hartman, ed.), p. 367. North-

Holland. Amsterdam. †

22

Hartman, P. (1987). In: Morphology of Crystals. (I. Sunagawa, ed.). Part A, Chap 4.

Terrapub, Tokyo. †

Kern, R. (1967). Rost. Kristallov. 8, 5. †

Kubota, N., Mullin, J.W. (1995). A kinetic model for crystal growth from aqueous

solution in the presence of impurity. J. Cryst. Growth 152, 203-208

Kubota, N., Yokota, M. and Mullin, J.W. (2000). The combined influence of

supersaturation and impurity concentration on crystal growth. J. Cryst. Growth 212,

4805-488.

Malkin, A.I., Chernov, A.A. and Alexeev, I.V. (1989). Growth of dipyramidal face of

dislocation-free ADP crystals; free energy of steps. J. Cryst. Growth 97, 765-769.

Martins, P.M. and Rocha, F. (2007). Characterization of crystal growth using a spiral

nucleation model. Surf. Sci. 601, 3400-3408.

Martins, P.M., Rocha, F. and Rein, P. (2006). The influence of impurities on the crystal

growth kinetics according to a competitive adsorption model. Cryst. Growth Des. 6,

2814-2821.

Ohara, M. and Reid, R.C. (1973). Modelling Crystal Growth Rates from Solution.

Prentice-Hall, New Jersey.

Oscik, J. (1982). Adsorption. PWN, Warsaw.

Sangwal, K. (1994). In: Elementary Crystal Growth (K. Sangwal, ed.), Chap. 4. Saan,

Lublin. †

Sangwal, K. (1996). Effects of impurities on crystal growth processes. Progress in Crystal

Growth and Characterization of Materials. 32, 3-43. †As cited by K. Sangwal, (1996). Prog. Crystal Growth and Charact. 32, 3-43.


Batch Crystal Growth Experiments Batch Crystal Growth Experiments Batch Crystal Growth Experiments Batch Crystal Growth Experiments in Pure and Impure in Pure and Impure in Pure and Impure in Pure and Impure

SolutionsSolutionsSolutionsSolutions

3.1. Sucrose

The sucrose used in the present study was obtained from the RAR sugar refineries,

Portugal. The sucrose obtained was 99.95% pure and was directly used in crystal growth

experiments without any further purification. Sucrose solutions of desired supersaturation

were prepared by dissolving the sucrose crystals in ultrapure water depending on the

working temperature conditions.

3.2. Surfactant

In the present study, Hodag CB-6 was obtained from RAR sugar refineries, Portugal.

Hodag CB-6 is alpha methyl glucoside ester mixture based on fatty acids from coconut

oil which is a mixture of unspecified mono-, di-, tri-, etc. esters. Hodag is a trademark of

Lambent Technologies Corporation, IL, USA. Hodag CB-6 KP is a 100% organic active

antifoam used in the processing of sugar. Hodag CB6 is used in sugar crystallization to

lower the viscosity of sugar by-products (C massecuite and molasses) and also, by this

way, improving the separation of C sugar in the centrifugals. The surfactant was used

directly as obtained, in the crystal growth experiments without any modifications.

3.3. Crystal growth experiments

Growth of sucrose crystals in pure and impure solutions were made in a 4L batch agitated

crystallizer at different temperatures (30, 40 and 50 oC). The operating variables studied

were the surfactant concentration and temperature. The crystallizer was connected to the

online monitoring system for continuous monitoring of Brix, defined by the percentage of

sucrose in solution, and temperature as shown in Fig. 3.1. The temperature inside the

crystallizer was maintained by crystallizer jacket which is connected to a thermostatic

water bath. Unless specified, agitation inside the crystallizer was maintained at a constant

agitation speed of 250 RPM. Sucrose solution was done by dissolving the sucrose crystals

at Tw+20oC in ultra pure water. Tw refers to the working temperature. In all the cases the

24

impurity was added while dissolving the sucrose at (Tw+20) oC. Crystal growth

experiments were carried out in the presence of surfactant ranging from 0.063 to 0.254

g/L of H2O, 0.067 g/L of H2O to 0.268 g/L of H2O and 0.0713 to 0.356 g/L of H2O at 30,

40 and 50 oC, respectively. Supersaturation was obtained by cooling down the solution to

working temperature. All the experiments were carried out for an initial supersaturation

of 20 g of sucrose/100 g of water. Once the crystallizer temperature was stable,

accurately weighed amount of 16 g of sucrose seed crystals was added into the

crystallizer. Unless specified, all the crystal growth experiments in the presence of

impurities were carried out with seed crystals of diameter 0.0536 cm. The crystal growth

experiments were carried out for 24 to 72 hours based on the solution temperature. After

24 or 72 hours, the solution reaches a supersaturation roughly of about 7 g of sucrose/100

g of water.

Fig. 3.1. Batch crystallizer: R: Refractometer; s: seeds; A: agitator; t: thermocouple.

Assuming no spontaneous nucleation and crystal breakage, the mass of the

crystals inside the crystallizer at any time was calculated from mass balance. The crystal

growth kinetics was estimated from the change in the mass of crystals, ∆m, with respect

to a given interval ∆t. For any time interval ∆t, the linear growth rate of sucrose crystals,

R, considering constant supersaturation, was given by (Mullin, 1993):

25

( ) tNf

MMR

cv

initialfinal

∆

−=

3/1

3/13/1

ρ (3.1)

Mfinal and Minitial are the mass of final and initial crystals in the crystallizer corresponding

to the time interval ∆t, fv and cρ are the volume shape factor and density of the sucrose

crystals, respectively, and t is the time. N is the number of growing crystals.

The kinetic parameters were estimated based on the R values corresponding to the

supersaturation changing from 20 to 7 g of sucrose/100 g of water. For the studied seed

crystals diameter, the constants in the denominator of Eq. (3.1) are given by (Guimarães

et al., 1995; Bubnik and Kadlec, 1992):

( )cmg

Nf cv

3/13/1

0213.01 −=

ρ (3.2)

The overall growth rate, Rg, can be determined using Eq. (3.1) after introducing the shape

factors for the sucrose crystals

Rf

fR

s

cvg

ρ3= (3.3)

fs is the area shape factor. N, assumed constant, was predicted using the expression

(Bubnik and Kadlec, 1992):

( )3ocv

o

Lf

mN

ρ= (3.4)

where, mo and Lo represent the mass and characteristic size of seed crystals, respectively.

In this study, fv and fs are 0.64 and 4.52, respectively, while the sucrose density, cρ , is

1.581 x 103 kg/m3. The Lo in Eq. (3.4) was determined using Coulter particle size

analyzer (Coulter LS230).

3.4. Image analysis

The microscopic pictures of the dried samples were obtained using a transmitted light

microscopy (Leica DMLB) with a monochrome camera (Leica DC 100) connected to PC,

where 8-bit grey level images of 768 x 576 square pixels are captured. VisilogTM5

(Noesis, Les Ulis, France) was used to analyse the captured images. These images are

then treated, analyzed and several numerical descriptors are extracted for each crystal

using VisilogTM5 (Noesis, les Ulis, France).

26

3.5. References

Bubnik, Z. and Kadlec, P. (1992). Sucrose crystal shape factor., Zuckerind. 117, 345-350.

Guimarães, L., Sá, S., Bento, L.S.M. and F. Rocha. (1995). Investigation of crystal

growth in a laboratory fluidized bed. Int. Sugar J. 97, 199-204.

Mullin, J.W. (1993). Crystallization, Butterworth-Heinemann, Great Britain.

Chapter 4

Studies on the effects of a non-ionic surfactant on the growth

kinetics of sucrose crystals

Abstract

Experiments were carried out in batch process to study the effect of Hodag CB6, a non-

ionic surfactant on the growth kinetics of sucrose crystals at 30 and 50 oC. The operating

variables studied were the supersaturation, impurity concentration and temperature. The

growth rate of sucrose crystals was found to increase with impurity concentration. The

transient kinetics of the growth process was analyzed using the multiple nucleation model

and a parabolic BCF diffusion model. A multiple nucleation model was found to be

successful in representing the kinetics of sucrose crystal growth process for the range of

impurity concentrations studied at 30 and 50 oC. Kinetic studies showed that the growth

promoting effect was due to the decrease in the surface free energy due to the addition of

surfactant. The surface free energy was calculated using the multiple nucleation model

and was found to be decreasing with increasing impurity concentration. The growth

process was influenced by both the kinetic growth inhibition effect and the

thermodynamic effect; however thermodynamic effect was the dominant step for the

range of impurity concentrations studied. The coverage of impurity molecules on the

sucrose surface follows a Henry type isotherm at 30 and 50 oC. The multiple nucleation

model was used to determine the kinetics, thermodynamic and morphological parameters

of the sucrose crystals for the range of impurity concentrations studied. In the case of

pure system, the total kink density was found to be 9.20 x 1015 kinks/m2 and 4.39 x 1015

kinks/m2 at 30 and 50 oC, respectively. The mean linear growth rate of sucrose crystals in

pure solutions was found to be 5.58 x 109 and 1.36 x 1010 crystal monolayers/s at 30 and

50 oC, respectively. The active growth sites on the crystal surface were found to be 3

orders of magnitude less than the total number of sucrose molecules.

4.1. Introduction

The effect of impurity in the supersaturated solution will significantly interfere with the

growth rate, nucleation, morphology and the agglomeration rate of the crystals. The

28

kinetics of crystal growth from aqueous solution is a very complex process, because of

the multiple steps (diffusion and integration) involved. The presence of impurity may

play a significant role in either of these steps (Sangwal, 1999). The presence of impurities

also showed a significant alteration in the morphology of the growing crystals

(Murugakoothan et al., 1999; Sangwal, 1993, 1996). Several works have been reported

dealing with the effect of impurities on the growth kinetics of crystals in solutions

(Murugakoothan et al., 1999; Sangwal, 1996; Sangwal, 1993; Sangwal, 1999;

Kuznetskov et al., 1998; Sangwal and Brzóska, 2001a; Kubota et al., 2001; Sangwal and

Brzóska, 2001b). The impurities either increase or decrease the growth rate of crystals

depending on the surface properties of the crystal, impurity and also on the solute. Some

impurities may exhibit selective influence on a particular crystallographic face

(Sgualdino et al., 2006; Sgualdino et al., 2000; Sgualdino et al., 1998; Murugakoothan et

al., 1999). The impurities intensively added to either alter the growth rate of growing

crystals or to modify the crystallographic structure are in general called as additives. The

effects of additives can be classified as thermodynamic effects or kinetic effects (Al-

Jibbouri et al., 2002). Many investigations are being carried out to explain the effect of

impurity on the growth kinetics for several crystallization systems mainly focusing on the

kinetics effects of impurities (Al-Jibbouri et al., 2002; Sgualdino et al., 2006; Martins et

al., 2006). Only few studies are dedicated towards the thermodynamic effects due to the

addition of impurities. The inhibiting effects of additive or impurity on the growth of

crystals are usually modeled based on the mechanism of impurity sorption in kinks and in

terrace considering the kinetic effects (Al-Jibbouri et al., 2002). The increase in growth

rate was usually modeled considering the thermodynamic effect which is due to the

decrease in surface energy by adsorption of impurity on growing surface (Davey, 1976;

Sangwal and Brzóska, 2001 a,b; Kuznetskov et al., 1998). In the present study, the

surfactant Hodag CB6 showed a growth promoting effect on the growth of sucrose

crystals.

Several kinetic models were used in literature to explain the kinetics and

thermodynamic effects of the impurities on the crystal growth process. Kubota-Mullin

(Kubota, 2001) and Cabrera-Vermilyea (1958) models are the most widely used kinetics

to explain the inhibiting effect of the impurities on the crystal growth process. Very

29

limited studies are available in literature explaining the growth promoting or the

thermodynamic effect of impurities on the growth kinetics of crystals. BCF surface

diffusion model, multiple nucleation model and a model involving the complex source of

cooperating dislocations were found to be excellent in explaining the kinetic and

thermodynamic effects simultaneously. A review on these kinetics models was made by

Sangwal (1996).

In the present study the growth promoting effect of Hodag CB6 on the kinetics of

sucrose crystal growth was studied as a function of supersaturation, temperature and

impurity concentration. In the present study, the BCF diffusion model and the multiple

nucleation or the birth and spread model were used to understand the effect of a non-ionic

surfactant on the growth kinetics of sucrose crystals.

4.2. Experimental

Growth of sucrose crystals was carried out in a 4 L batch agitated crystallizer (Fig. 3.1) at

two different temperatures, 30 and 50 ºC. Crystals, ranging within the sieve fractions

0.0425 to 0.0500 cm, were used as seed crystals. The average seed size was determined

using a laser size analyzer (Coulter LS230) and was found to be 0.0536 cm. Crystal

growth experiments were carried out in the presence of impurity ranging from 0.063 to

0.254 g/L of H2O and 0.0713 to 0.356 g/L of H2O at 30 and 50 oC respectively.

Experiments in the absence of impurity were also made. The experiments were carried

out for 24 to 72 hours, depending on the solution temperature, until the supersaturation

reaches 7 g of sucrose/100 g of water, approximately. The mass of the crystals inside the

crystallizer at any time was calculated from mass balance as explained in section 3.3.

4.3. Results and discussions

Figs. 4.1a and 4.1b show the change in linear growth rate as a function of supersaturation

for different impurity concentrations at 30 and 50 oC respectively. From Figs. 4.1a and

4.1b, it can be observed that the growth rate of sucrose crystals was greatly influenced by

the added impurity at the studied temperatures for the range of impurity concentrations

studied. Further it can be observed that at both 30 and 50 oC, the added surfactant

promotes the growth rate of sucrose crystals and the growth rate of sucrose crystals was

found to be increasing with increase in impurity concentration. A similar effect was

previously reported for the growth of ammonium oxalate monohydrate crystals

30

0

0.000000005

0.00000001

0.000000015

0.00000002

0.000000025

0.00000003

0.000000035

0.00000004

0 0.02 0.04 0.06 0.08 0.1

σ (−)σ (−)σ (−)σ (−)

R,

m/s

ci: 0.063 g/L of water




Fig. 4.1a. Plot of linear growth rate versus supersaturation ratio for different impurity concentrations at 30 oC. in presence of Fe (III) ions (Sangwal and Brzóska, 2001a). The growth promoting effect

can be explained on the basis of reduction in the surface energy due to the adsorption of

surfactant molecules at the kink sites (Davey, 1976; Sangwal and Brzóska, 2001a,b). The

growth promoting effect due to the added impurity is usually called as the

thermodynamic effects of impurities (Al-Jibbouri et al., 2002; Sangwal, 2008). The

decrease in surface free energy increase the step velocity and the increase in step velocity

refers to the kinetic effect and can be studied from the increase in the kinetic constant in

the case of growth promoting conditions due to impurities.

31

0

0.00000001

0.00000002

0.00000003

0.00000004

0.00000005

0.00000006

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

σ (−)σ (−)σ (−)σ (−)

R,

m/s

Pure






Fig. 4.1b. Plot of linear growth rate versus supersaturation ratio for different impurity concentrations at 50 oC.

In order to understand the growth promoting effect and also to know about the

incorporation of impurities into the crystal lattice, the sucrose crystals grown in the

presence of impurities were analyzed using FTIR. Figs. 4.2a-4.2c show the FTIR spectra

of Hodag CB6, pure sucrose crystals, sucrose crystals from growth experiments in

presence of surfactant, respectively. From the absorption spectra, it can be observed that,

the crystals from the growth experiments in the presence of additives do not show any

characteristic peaks corresponding to C-O groups and O-H groups in the surfactant

molecules. This observation shows that there is no incorporation of the organic impurity

during the growth of sucrose crystals.

Previously several studies have been carried out to explain the inhibiting and

promoting effect of impurities on the growth of crystals using several theoretical models

32

Fig. 4.2a. FTIR spectrum of Hodag CB6.

Fig. 4.2b. FTIR spectrum of pure sucrose.

33

Fig. 4.2c. FTIR spectrum of sucrose grown in solution with impurity (Hodag CB6).

Table 4.1. Fitted kinetic parameters according a power law growth kinetics.

30 ºC 50 ºC

ci, g/L of

water K, m/s n r2

ci, g/L of

water K, m/s n r2

0 5.00E-06 2.50 0.9889 0 0.0007 3.68 0.973

0.063 0.0004 4.02 0.989 0.071 0.0002 3.15 0.9844

0.127 0.0001 3.35 0.9907 0.142 2.00E-05 2.34 0.9967

0.190 0.0001 3.42 0.9893 0.213 4.00E-05 2.50 0.9968

0.254 8.00E-05 3.22 0.9917 0.285 3.00E-05 2.51 0.9923

0.356 3.00E-05 2.46 0.9974

(Sangwal and Brzoska, 2001a,b; Sangwal, 1999; Davey, 1976; Kubota, 2001).

Considerable amount of works are reported considering the kinetic effect of the

impurities on the growth process and only few studied were made about the

thermodynamic effects of the added impurities on the growth kinetics. Kubota-Mullin

(Kubota, 2001) and the Carbrera and Vermilyea (1958) models are the widely used

models to explain the growth inhibition kinetics due to the impurities in solutions.

34

However these models cannot help to simultaneously explain both the kinetic and the

thermodynamic effects of impurities during the crystal growth process (Sangwal, 2003).

Instead, the theoretical growth kinetics that incorporates the thermodynamic and kinetic

parameters would be more useful to study the effect of thermodynamics and kinetics

simultaneously.

In the present study, the growth promoting effects of the surfactant or the

thermodynamic effect and the kinetic effects were studied simultaneously using the BCF

surface diffusion model and birth-spread or multiple nucleation model.

4.3.1. Multiple nucleation model

The transient kinetic behaviour of the growth process in the presence of additive

following a multiple nucleation model is given by (Mullin, 2001; Sangwal, 2008):

−=σ

σ FAR o exp6/5 (4.1)

where, the constants Ao and F in B-S model are given by Eqs. (4.2) and (4.3)

respectively:

( ) 3/12soo anhhcA Ω= β (4.2)

hom2

2

*.3 DGX

kThF ∆=

Ω= γπ (4.3)

Where, h is the height of elementary steps (m), co is the solubility of sucrose at

temperature, T (K), Ω is the specific molecular volume (m3), a is the dimension of

growth units normal to the step, γ is the surface free energy (J/m2) and hom2* DG∆ is the

free energy change required for the formation of stable two-dimensional nuclei on a

perfect surface.

The linearized expression of Eq. (4.1) is given by:

( )σσF

AR

o −=

lnln6/5

(4.4)

Thus the constants F and Ao can be predicted from the slope and intercept of the linear

plot of

6/5

lnσ

R versus

σ1

. Figs. 4.3a and 4.3b show the plot of

6/5

lnσ

R versus

σ1

at

35

30 and 50 oC respectively. The calculated constant, F, can be used to obtain the surface

free energy, γ , theoretically using Eq. (4.3).

Figs. 4.3a and 4.3b show the plot between

6/5

lnσ

R and

σF

for the range of

impurity concentrations studied at 30 and 50 ºC, respectively. The calculated constant F

calculated from the slope according to the multiple nucleation model plotted against the

impurity concentration is shown in Fig. 4.4a for the growth experiments carried out at 30 oC. From Fig. 4.4a, it can be observed that the constant F decreases with increase in the

impurity concentration. This was in agreement with the theory that the increase in growth

rate could be due to the decrease in surface free energy due to the adsorption of

impurities at the kink sites.

-12

-11

-10

-9

-8

-7

-6

0 5 10 15 20 25 30 35 40

1 /σ1 /σ1 /σ1 /σ

Ln

(R/ σσ σσ

5/6 ),

cm

/min

Pure

ci: 0.063 g/L of w ater




Fig. 4.3a. Experimental data and the birth spread kinetics for the growth of sucrose crystals for different impurity concentrations at 30 oC.

36

From Fig. 4.4a, it can be also observed that, at 30 oC, the predicted F value for pure

system was found to be lower than for the experiments performed in the presence of

impurities. However, it can be observed that the growth rate of sucrose crystals increases

with increase in growth rate. The lower F value in the case of pure system could be due

to the influence of the kinetic order on the determined parameters while fitting by the

method of least squares. Table 4.1 shows the kinetic constant, K, and the order and the

corresponding r2 value according to a semi empirical expression given by:

nKR σ= (4.5)

-9

-8.5

-8

-7.5

-7

-6.5

-6

-5.5

10 15 20 25 30 35

Ln

(R/ σσ σσ

5/6 )

, cm

/min

1111 /σ/σ/σ/σ

Pure ci: 0.071 g/L of water

ci: 0.142 g/L of water ci: 0.213 g/L of water

ci: 0.285 g/L of water ci: 0.356 g/L of water

Fig. 4.3b. Experimental data and the birth spread kinetics for the growth of sucrose crystals for different impurity concentrations at 50 oC.

From Table 4.1, it can be observed that the n value was found to be very higher, at 30 ºC,

for impure system when compared to the growth of pure sucrose crystals. The order of

kinetics can influence the magnitude of slope and intercept of the multiple nucleation

37

model and also on determined kinetic parameters while using the method of least squares.

Thus, in the present study, assuming that the surface free energy decreases with increase

in impurity concentration, for the growth experiments at 30 oC, a relation between

impurity concentration and the F was proposed and it fits the linear expression with an r2

value of 0.756:

0.2569-0.6265cF i += (4.6)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

ci, g/L of water

F

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Ao,

cm/m

in

Eq(4.6)

Fig. 4.4a. Plot of F and Ao versus impurity concentration, ci, for the growth experiments at 30 oC.

The relation between F and ci at 50 oC fits the relation with r2 value of 0.92:

38

0.1303-0.1569cF i += (4.7)

The kinetic constant Ao in the case of pure system at 30 oC was determined by assuming

F value obtained from Eq. (4.6) by minimizing the sum of the squared errors between the

experimental data and trend line (dotted line in Fig. 4.3a) and the corresponding Ao value

in the case of pure system was found to be 0.0418 cm/min. The calculated kinetic

constant Ao using the multiple nucleation model as a function of impurity concentration,

ci, for the growth experiments at 30 oC is shown in Fig. 4.4a. From Fig. 4.4a, it can be

observed that the constant Ao decreases with increase in impurity concentration at the

studied temperatures.

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

ci. g/L of water

F

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

Ao,

cm/m

in

Eq (4.7)

Fig. 4.4b. Plot of F and Ao versus impurity concentration, ci, for the growth experiments at 50 oC.

39

Assuming the growth unit normal to steps equal to the height of the elementary

steps in Eq. (4.2), the constant Ao can be determined as a function of kinetic coefficient of

steps, β, which is independent of impurity concentration, ci, given by (Sangwal and

Brzóska, 2001a):

β3/13/23/5soo ncaA Ω= (4.8)

Thus the variation of Ao in Fig. 4.4a with the increasing impurity concentration is due to

the variation in kinetic constant, β, or otherwise the activation energy W for growth.

From the value of Ao and F, it could be concluded that the increase in the growth rate in

the presence of impurity is due to the decrease in the free energy of the surface due to the

adsorption of impurities on the kink sites leading to a decrease in step height to step

distance ratio. However the decrease in both Ao and F clearly indicates the combined

effect due to the thermodynamics and kinetics with increase in impurity concentration. A

similar effect was previously reported for the growth of 001 face of ammonium oxalate

monohydrate in presence of Cu(II) ions (Sangwal and Brzóska, 2001a). The increase in

growth rate with respect to the impurity concentration suggests the domination of

thermodynamic effect over the kinetic effect of Hodag CB6 on the growth kinetics of

sucrose crystals. The reduction in the surface free energy can be calculated theoretically

from the multiple nucleation kinetics from F using Eq. (4.3). The relation between the

impurity concentration, ci (g/L of water), and the surface energy γ, at 30 oC, fits the

following equation with r2 value of .995

0.0056 + -0.0084ci=γ (4.9)

By multiple nucleation model, the surface tension for pure system at 30 oC was found to

5.58 x 10-3 J/m2.

Assuming 3/1Ω=h and using 3301004.715 m−×=Ω (Martins and Rocha, 2007),

the surface free energy as a function of impurity concentration can be obtained from the

determined F value. Representing the surface free energy of pure sucrose crystal byoγ ,

the rate of decrease in the free energy with respect to the added impurities fits the

empirical relation:

)1( iio ck−= γγ (4.10)

40

The physical meaning of Eq. (4.10) can be obtained by rewriting Eq. (4.3) in terms of

surface free energy and assuming( ) 2/12/1/3 FF ≈π ;

( ) ( ) ( )iio ck

kT

h

kT

h −Ω

=Ω1

2/12/1 γγ (4.11)

From the definition of the constant F, Eq. (4.11) can be written as

( )iipop ckGG −∆=∆ 12/1*2/1* (4.12)

For very low impurity concentrations, as is the case of present investigation, the change

in free energy for the formation of stable nucleus in pure and impure solution as a

function of impurity concentration can be obtained from Eq. (4.12) as

′−∆=∆ iipop ckGG 1** (4.13)

where ii kk 2=′ . According to Eq. (4.13), the free energy change *G∆ decreases with

increase in impurity concentration ci. Eq. (4.13) is analogous to the three dimensional

nucleation (Mullin, 2001; Sangwal, 2008): hom22 ** DDhet GG ∆=∆ φ , where the factor φ is

less than or equal to unity. The factors hom2* DG∆ and DhetG 2*∆ represent the energy

required for homogeneous and heterogeneous nucleation. The rate of nucleation of

solution can be affected considerably by the presence of impurities in the system. The

presence of impurity can induce the nucleation at degrees of super cooling less than that

required for spontaneous nucleation (Mullin, 1993). In the present case from Eq. (4.13),

the factor

′−= ii ck1φ obviously is less than unity and decreases with increase in

impurity concentration. Thus, in the presence of impurities Eq. (4.10) can be used to

study the effect of impurities on the thermodynamics by considering the constant F of

multiple nucleation model (Sangwal, 2008). Fig. 4.5 shows the excellent fit between oγγ /

and ci according to Eq. (4.10).

Eq. (4.10) is similar to the Shishkovskii’s empirical expression given by (Sangwal,

2008):

( )]1ln1[ θγγ −−= Bo (4.14)

where θ is the surface coverage of the impurity and B is a constant given by:

41

mo

kTB

ωγ= (4.15)

For low impurity concentrations, ln( ) iLcK==− θθ1 , and in this case Eq. (4.10) can be

written as:

]1[ iLo cBK−= γγ (4.16)

6.00E-01

6.50E-01

7.00E-01

7.50E-01

8.00E-01

8.50E-01

9.00E-01

9.50E-01

1.00E+00

0 0.1 0.2 0.3 0.4

γ/γ

γ/γ

γ/γ

γ/γ οο οο

ci, g/L of water

30 ºC

50 ºC

Fig. 4.5. Shishkovskii isotherm for Hodag CB6 onto sucrose particles.

where, KL is the Langmuir constant given by (Sangwal and Brzóska, 2001a,b, Sangwal,

2008):

=

RT

QK diff

L exp (4.17)

R is the gas constant and Qdiff is the differential heat of adsorption of the impurity on the

surface.

42

Thus, according to Eqs. (4.8) and (4.10), the multiple nucleation model can be used to

model both the kinetic and thermodynamic effects of the impurity.

Assuming the Langmuir isotherm for the sorption of impurity onto the sucrose

crystals, the effect of impurity on the growth kinetics can be modeled by rearranging the

empirical Eq. (4.10) as:

iio

ck−= 1γγ

(4.18)

The constant ki can be calculated from the plot of oγ

γ versus ci as shown in Fig. 4.5a.

Comparing Eqs. (4.16) and (4.10), the constant Langmuir constant, KL, is given by:

kT

kK moi

L

ωγ= (4.19)

The surface area per adsorbed molecule, lies between 0.2 – 0.4 nm2. In the present study,

mω was assumed as 0.3 nm2. The calculated KL value for the sorption of impurity onto

sucrose crystals at 30 oC was found to be 0.522 L/g. For lower solute concentration, the

surface coverage, θ, according to Langmuir isotherm can be calculated using the KL

value.

The constants Ao and F for different impurity concentrations at 50 oC were

calculated from the intercept and slope of Fig. 4.3b. Fig. 4.4b shows the plot of F versus

impurity concentration for the crystal growth experiments carried out at 50 oC. From Fig.

4.4b, it can be observed that the F value was found to be decreasing with increase in

impurity concentration. The deviation from linearity may be due to the influence of the

kinetic order on the magnitude of the slope while using the linear regression technique.

Assuming that the surface energy decreases with increase in impurity concentration, the

surface energy for an impurity concentration of 0.142 g/L of water was found to be 3.87 x

10-3 J/m2. The change in surface energy with increasing impurity concentration follows

the expression with r2 0.9296:

0042.00029.0 +−= icγ (4.20)

The value of Ao, when ci = 0.142 g/L of water was obtained by minimizing the sum of the

squared errors between experimental data and trend line (dotted line in Fig. 4.3b)

assuming γ given by Eq. (4.20). The calculated Ao values as a function of impurity

43

concentration is shown in Fig. 4.4b. From Fig. 4.4b, it can be observed that the Ao values

decrease with increasing impurity concentration. This shows the combined

thermodynamic and kinetic effect of the added surfactant on the growth kinetics of

sucrose crystals. The Langmuir constant KL for the sorption of impurity on the crystal

surface at 50 oC can be obtained from the plot between oγ

γ and ci using Eqs. (4.7) and

(4.18) as shown in Fig. 4.5. The Langmuir constant KL value at 50 oC was determined

from the slope of Fig. 4.5 and was found to be 0.221 L/g. The determined KL values were

used to calculate the surface coverage of impurities onto the sucrose crystals using a

Langmuir isotherm at studied temperatures and are shown as a function of ci in Fig. 4.6.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

θθ θθ

ci, g/L of water

30 ºC

50 ºC

Fig. 4.6. Surface coverage versus surfactant concentration at 30 and 50 ºC.

The KL value can be used to determine the Gibbs free energy and other thermodynamic

parameters using Eqs. (4.21) to (4.23) (Gupta et al., 2008)

( )LKRTG ln−=∆ (4.21)

44

−∆−=

12

2 11ln

1TTR

H

K

K

TL

TL (4.22)

STHG ∆−∆=∆ . (4.23)

In the present study, molecular weight of the surfactant used was assumed to be

14,000. Molecular weight of 14,000 was assumed from the value of molecular weight of

PluronicTM F 108 which has a similar composition to that of HodagTM Non-ionic (Ref:

US patent 6555544). As no information was available about the molecular weight of the

surfactant Hodag CB6 used in the present study, thermodynamic parameters for the

sorption of impurity onto the sucrose surface were calculated with this assumption. The

calculated G∆ , H∆ and S∆ for the sorption of surfactant molecules onto the sucrose

surface are given in Table 4.2. From Table 4.2, the negative H∆ value shows the

sorption of surfactant molecules onto the sucrose surface is an exothermic process. The

decrease in G∆ with increasing temperature suggests that the decrease in the surface free

energy with respect to added impurity was predominant at lower temperature.

Figs. 4.4a and 4.4b show that the constant Ao was found to be decreasing with increase in

impurity concentration at 30 and 50 oC, respectively. At constant temperature, the

constant Ao can be related with the surface density of the adsorbed molecules as:

3/1

,

,

,

,

=

pures

impuritys

pureo

impurityo

n

n

A

A (4.24)

Table 4.2. Thermodynamic parameters for the sorption of surfactant onto sucrose surface T, K KL, L/g ∆∆∆∆G, kJ/mol ∆∆∆∆H, kJ/mol ∆∆∆∆S, kJ/mol 303 0.522 -22.4 -28.3

-0.354 323 0.221 -21.6

Fig. 4.7 shows the plot of pures

impuritys

nn

,

, versus ci at 30 and 50 oC. From Fig. 4.7, it can

be observed that the pures

impuritys

nn

,

, value was higher at 50 oC for the range of impurity

concentrations studied. This indicates the growth promoting effect was higher at 50 oC.

This was on controversy with the G∆ value at 30 and 50 oC, which indicates the complex

45

mechanism behind the growth process in presence of additives. However, a possible

reason for the higher growth promoting effect at 50 oC and a decrease in G∆ for

adsorption of impurity onto sucrose surface could be due to the domination of the kinetic

inhibition at 30 oC.

The step kinetic coefficient for the growth of crystals for different concentrations of

impurities was calculated using Eq. (4.2). Upon substituting the values for the parameters

in Eq. (4.8), the kinetic constant, β, can be related with the constant Ao as:

βoo cA 271087.5 −×= (4.25)

where, co is the solubility of sucrose at temperature T (3.76 x 1027 and 4.53 x 1027

molecules/m3 of water).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4

ns,

imp

uri

ty/n

s,pu

re

ci, g/L of water

30 ºC 50 ºC

Fig. 4.7. Ratio of surface density of the adsorbed molecules versus impurity concentration.

46

Using Eq. (4.25), the kinetic constant, β, can be obtained which enables to calculate the

activation energy, W, from ( )kTWav −= expβ and v = kT/hp (where hp is the Planck’s

constant).

The calculated kinetic constant, β, and the activation energy for the step growth, W, for

the range of impurity concentrations studied at 30 and 50 oC are given in Table 4.3. The

activation energy was found to be in the range of 44-49 and 47-48 kJ/mol at 30 and 50 oC, respectively. The activation energies lying in the range of 40-60 kJ/mol show that

growth process was limited by surface integration mechanism (Mullin, 1993).

Table 4.3. Kinetic constant and activation energy by multiple nucleation model.

30 ºC 50 ºC ci,g/L ββββ,,,, m/s W, kJ/mol ci,g/L ββββ, m/s W, kJ/mol

0 1.54 x 10-4 43.9 0 5.15 x 10-5 46.6 0.063 7.12 x 10-5 45.8 0.071 4.57 x 10-5 46.9 0.127 2.22 x 10-5 48.8 0.142 4.32 x 10-5 47.1 0.190 1.87 x 10-5 49.2 0.213 3.10 x 10-5 47.9 0.254 1.74 x 10-5 49.4 0.285 2.91 x 10-5 48.1

0.356 2.89 x 10-5 48.1

4.3.2. BCF surface diffusion model

The growth rate of crystals according to a BCF surface diffusion model is given by

(Burton et al., 1951)

( )σσ

σσσ/

/tanh

1

1cR = (4.26)

Eq. (4.26) can explain the growth process if the kinetics was controlled by surface

diffusion.

1σ is given by:

skTλγσ Ω= 5.9

1 (4.27)

and the constant, c, in Eq. (4.26) is given by:

ββ

ΩΛ=

a

nc o1 (4.28)

47

where, 1β and Λ are dimensionless factors less than unity describing the influence of the

steps and the kinks in steps, respectively. no is the concentration of growth units on the

surface (particles/m2), Ω is the specific molecular volume of molecule or atom (m3), a is

the dimension of the growth unit normal to the advancing step (m), sλ is the average

diffusion distance of the growth units on the surface (m), k is the Boltzmann constant,

and T is the temperature, K.

Assuming Λ1β equal to unity, according to Burton-Cabrera-Frank model one obtains:

∆−Ω=

kT

Gvnc ads

o exp (4.29)

where ∆Gads is the total adsorption energy which is the sum of adsorption energy factors:

from the solution to the surface and from the surface to the kink where the growth unit is

incorporated into the crystal surface. The parameter on refers to the number of molecular

positions available for adsorption on the crystal surface, given by

m

sucrosesucrose

m

toto A

mSSA

A

An == (4.30)

where Atot is the total surface area of the sucrose crystals available for the growth of

crystals in supersaturated solution, SSAsucrose is the specific surface area of the sucrose

crystals and msucrose is the mass of seed crystals and Am is the area occupied by one

molecule and is equal to 3/2Ω . The specific surface area of sucrose can be calculated from

BET analysis. Assuming phkTv /= (hp refers to Planck’s constant), the Gibbs free

energy for adsorption of sucrose molecule from solution onto the crystal surface and

incorporation into a kink can be calculated by rearranging the Eq. (4.29)

vn

ckTG

oads Ω

−=∆ ln (4.31)

When σσ 1 >>1, the growth law exhibits non-linear behavior given by:

2

1

σσc

R = (4.32)

Using the kTγ value from multiple nucleation model, the BCF expression can be

solved to analyze the kinetic effect of the added impurity on the growth kinetics. A non-

48

linear regression technique was used to solve Eq. (4.32). The non-linear regression

involves the maximization of coefficient of determination between the experimental data

and Eq. (4.32) using solver add-in, Microsoft Excel, Microsoft Corporation. Figs. 4.8a

and 4.8b show the experimental data and predicted BCF surface diffusion kinetics by

non-linear regression analysis at 30 and 50 oC respectively. The r2 between the

experimental data and the predicted BCF kinetics at 30 and 50 oC for the range of

impurity concentrations studied is given in Table 4.4.

Table 4.4. Energy of adsorption for the sorption of sucrose molecules onto the crystal surface determined by BCF theory. 30 ºC 50 ºC

ci, g/L of water∆∆∆∆Gads, kJ/mol r2 ci, g/L of water ∆∆∆∆Gads, kJ/mol r2 0 83.9 0.9666 0 93.5 0.8544

0.063 82.9 0.7461 0.071 86.3 0.9084 0.127 82.4 0.7572 0.142 86.5 0.9717 0.190 82.6 0.8033 0.213 86.4 0.9724 0.254 83.0 0.8289 0.285 86.4 0.9263

0.356 86.4 0.9707

From Table 4.4, it can be observed that the experimental data was well represented by

BCF diffusion model at 50 oC with r2 > 0.9. In the case of 30 oC, the BCF model poorly

represents the experimental data. Nevertheless the predicted constants were found to be

useful in predicting the mechanism of the growth kinetics. In this study, the surface free

energy determined from the multiple nucleation model was used to determine the

constant 1σ for the range of impurity concentrations studied. The predicted c value and

the constant 1σ are plotted against the impurity concentration as shown in Figs. 4.9a and

4.9b for the growth experiments carried out at 30 and 50 oC respectively. Figs. 4.9a and

4.9b show that, according to BCF model, there is no significant kinetic effect due to the

addition of surfactant on the growth kinetics. The growth promotion effect was found to

be mainly due to the thermodynamic effect, i.e., due to the decrease in interfacial tension.

The energy of adsorption for the sorption of sucrose molecules onto the crystal surface

was obtained using Eq. (4.31) and is given in Table 4.4. From Table 4.4, it can be

observed that there was no significant change in the adsorption energy for sucrose

49

molecules onto crystal surface due to the addition of surfactant for the range of impurity

concentrations studied. Table 4.4 shows that adsG∆ was in the range of 83 to 93 KJ/mol

for the range of impurity concentrations at studied temperatures.

0

5E-09

1E-08

1.5E-08

2E-08

2.5E-08

3E-08

3.5E-08

4E-08

0 0.02 0.04 0.06 0.08 0.1

R,m

/s

σσσσ

Pure





BCF

Fig. 4.8a. Experimental data and predicted BCF kinetics for the growth of sucrose crystals in pure and impure solutions at 30 oC.

The applicability of BCF and the Birth and Spread model suggests that the growth of

sucrose crystals is kinetically controlled by surface diffusion and the growth mechanism

is due to the incorporation of growth units into the crystal on spiral dislocations of the

sucrose surface. According to the Birth and Spread model, the growth promoting effect of

added surfactant was complex and associated with the decrease in both surface energy

and the kinetic coefficient.

In addition to the thermodynamic parameters, assuming one spiral on the crystal surface,

Birth-Spread model can be used to calculate several morphological parameters

(Koutsopolos, 2001).

50

0

1E-08

2E-08

3E-08

4E-08

5E-08

6E-08

0.03 0.04 0.05 0.06 0.07 0.08

R, m

/s

σσσσ

Pure





ci: 0.356g/L of water

BCF

Fig. 4.8b. Experimental data and predicted BCF kinetics for the growth of sucrose crystals in pure and impure solutions at 50 oC.

For a fixed supersaturation, the mean distance between two neighboring kinks of a spiral

step, xo (Koutsopoulos, 2001), and the critical radius of the spiral according to a BCF

model (Koutsopoulos, 2001) can be calculated using Eqs. (4.33) and (4.34) respectively.

= −

kTdSx ed

o

γexp2/1 (4.33)

( )SkT

ar ed

ln*

γ= (4.34)

where, edγ is the free edge work given by 2ded γγ = , and d is the diameter of the crystal

growth unit.

51

6.00E-02

7.00E-02

8.00E-02

9.00E-02

1.00E-01

1.10E-01

1.20E-01

0 0.05 0.1 0.15 0.2 0.25 0.3

ci, g/L of water

σσ σσ11 11

0.00E+00

1.00E-07

2.00E-07

3.00E-07

4.00E-07

5.00E-07

6.00E-07

c

Fig. 4.9a. Plot of σσσσ1 and c versus impurity concentration at 30 oC.

Using Eq. (4.34), the distance between the two neighbor steps of the spiral can be

calculated by

*4 ryo π= (4.35)

The kink density of the crystal surface can be calculated using Eq. (4.36) (Koutsopoulos,

2001)

( )( ) ( )kTkTa

SS

yx ededoo /exp/4

ln12

2/1

γγπ= (4.36)

52

5.00E-02

5.50E-02

6.00E-02

6.50E-02

7.00E-02

7.50E-02

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

ci, g/L of water

σσ σσ 11 11

0.00E+00

1.00E-07

2.00E-07

3.00E-07

4.00E-07

5.00E-07

6.00E-07

c

Fig. 4.9b. Plot of σσσσ1 and c versus impurity concentration at 50 oC.

At 50 oC, for a pure system at a supersaturation, σ , of 0.0738, the xo, rBCF, yo and 1/xoyo

values were found to be 1.87 x 10-9 m, 9.709 x 10-9 m, 1.22 x 10-7 m and 4.39 x 1015

kinks/m2, respectively. For the growth of pure sucrose crystals at 30 oC for a σ of 0.088,

the xo, rBCF, yo and 1/xoyo values were found to be 8.57 x 10-9 m, 1.01 x 10-8 m, 1.27 x 10-7

m and 9.20 x 1015 kinks/m2, respectively. Assuming the height of the spiral step is equal

to the height of unit cell, the mean rate of advancement of steps is given by

(Koutsopoulos, 2001) 3/1ΩR . The 3/1ΩR value for the growth of pure sucrose crystals

was found to be 5.58 x 109 and 1.36 x 1010 crystal monolayers/sec at 30 and 50 oC,

respectively. Fig. 4.10 shows the calculated 3/1ΩR values at 30 and 50 oC as a function

of impurity concentrations studied. The moles of sucrose on the crystal surface can be

53

calculated from the area occupied by one sucrose molecule, equal to the projection on the

surface. The area occupied by one sucrose molecule is given by:

3/2Ω=sucroseA (4.37)

5.00E-09

5.00E+09

1.00E+10

1.50E+10

2.00E+10

2.50E+10

0 0.1 0.2 0.3 0.4

R/ ΩΩ ΩΩ

1/3

ci, g/L of water

30 ºC

50 ºC

Fig. 4.10. Effect of impurity concentration on the mean rate of advancement of steps.

Thus the concentration of sucrose molecules on the crystal surface, Css, can be calculated

using Eq. (4.37) and was found to be 1.25 x 1018 molecules/m2. Comparing the Css with

1/xoyo, the active growth sites on the crystal surface were found to be 3 orders of

magnitude less than the total number of sucrose molecules. A similar observation was

previously reported during the growth of hydroxyapatite (HAP) crystals. In the case of

growth of HAP crystals, the active kink sites were found to be four times lower than the

total density of the kinks on the crystal surface. This mechanistic approach was found to

be useful in identifying the number of active sites that are involved in the crystal growth

54

process. In addition, using the calculated surface energy using the BCF model, the effect

of the surface energy due to the addition of impurity on 1/xoyo can be predicted

theoretically. In the present case, only a part of kink sites are actively involved in the

growth process and the most of them do not contribute in the crystal growth process as

they are located on the flat crystal area between the steps and spiral (Koutsopoulos,

2001).

4.4. Conclusions

The effect of non-ionic surfactant, Hodag CB6 on the growth kinetics of sucrose crystals

was studied at 30 and 50 oC for different impurity concentrations. The added impurity

increases the growth rate for the range of impurity concentrations at the studied

temperatures. The growth rate was found to be increasing with increase in impurity

concentration. The growth promoting effect of the added surfactant was studied using a

BCF surface diffusion model and a multiple nucleation model. A multiple nucleation

model well represents the experimental data with a coefficient of determination ranging

from 0.90 to 0.99 for the range of impurity concentrations studied. According to multiple

nucleation model, the surface free energy decreases with increase in impurity

concentration

The effect of added impurity on the growth kinetics was found to be complex and

was due to both thermodynamics and kinetics with the domination of thermodynamic

effect. The coverage of impurity molecules onto the sucrose surface follows a Henry

isotherm for the range of impurity concentrations studied at 30 and 50 oC. The parabolic

law or the BCF diffusion model poorly represents the experimental data at 30 oC,

however this model very well represents the experimental data at 50 oC for the range of

impurity concentrations studied. At 50 oC, according to BCF model the growth promoting

effect was due to the decrease in surface free energy with increasing impurity

concentration. In contrast to multiple nucleation model, BCF model suggests there is no

kinetic effect with increasing impurity concentration at 30 oC. The Gibbs free energy for

adsorption of sucrose molecule, adsG∆ , from solution onto the crystal surface and

incorporation into a kink was calculated using the kinetic constant from BCF model. No

significant change in the adsorption energy for sucrose molecules onto crystal surface

was observed due to the addition of surfactant for the range of impurity concentrations

55

studied. The parameters in the multiple nucleation model were used successfully to

determine the morphological parameters of the sucrose crystals. The kink density of the

crystal surface, the distance between two neighbor steps of the spiral, the critical radius of

the spiral and the mean distance between two neighboring kinks of a spiral step were

calculated using the surface free energy calculated using the multiple nucleation model

for different supersaturations. The active growth sites on the crystal surface were found to

be 3 orders of magnitude less than the total number of sucrose molecules.

56

4.5. References


influenced by pH-value and impurities., J. Cryst. Growth. 236, 400-406.

Bubnik, Z. and Kadlec, P. (1992). Sucrose crystal shape factor. Zuckerindindustrie. 117,

345-350.


equilibrium structure of their surfaces. Phil. Trans. Roy. Soc. London. 243, 299-358.

Cabrera, N. and Vermilyea, D.A. in: R.H. Domeus, B.W. Roberts, D. Turnbull, (Eds.),

Growth and perfection of crystals, Wiley, New York, 1958, p.393.

Davey, R.J. The effect of impurity adsorption on the kinetics of crystal growth from

solution, J. Cryst. Growth 34 (1976) 109-119.

Guimaraes, L., Sa, S., Bento, L.S.M. and Rocha, F. (1995). Investigation of crystal

growth in a laboratory fluidized bed, Int. Sugar J. 97, 199-204.

Gupta, V.K. and Rastogi, A. (2008). Equilibrium and kinetic modelling of cadmium(II)

biosorption by nonliving algal biomass Oedogonium sp. from aqueous phase. J.

Hazard. Mater. 153, 759-766.

Koutsopoulos, S. (2001). Kinetic study on the crystal growth of hydroxyapatite.

Langmuir 17, 8092-8097.

Kubota, N. (2001). Effect of impurities on the growth kinetics of crystals. Cryst. Res.

Technol. 36, 8-10


supersaturation and impurity concentration on crystal growth. J. Cryst. Growth. 212,

480-488.

Kumar, C. (1979). A new look at the BCF surface diffusion model. J. Cryst. Growth. 48,

489-490.



193, 164-173.


nucleation model. Surf. Sci. 601, 3400-3408.

57


kinetics according to a competitive adsorption model. Cryst. Growth Des. 6(12),

2814-2821.

Mullin, J.W. Crystallization, (1993), Third edition, Butterworth-Heinemann, Great

Britain.


Ramasamy, P. (1999). Habit modification of potassium acid phthalate (KAP) single

crystals by impurities. J. Cryst. Growth. 207, 325-329.

Sangwal, K. (1993). Effect of impurities on the processes of crystal growth, J. Cryst.

Growth. 28, 1236-1244.

Sangwal, K. (1996). Effects of impurities on crystal growth processes, Prog.

Cryst.Growth Charact. Mater. 32 (1996) 3-43.

Sangwal , K. (1999). Kinetic effects of impurities on the growth of single crystals from

solutions. J. Cryst. Growth. 203, 197-212.Sangwal K. (2008). Additives and

crystallization processes: From fundamentals to applications, John Wiley & Sons,

Ltd.


ammonium oxalate monohydrate crystals from aqueous solutions. J. Cryst. Growth

233, 343-354.

Sangwal, K. and Brzóska, M.E. (2001b). On the effect of Cu(II) impurity on the growth

kinetics of ammonium oxalate monohydrate crystals from aqueous solutions. Cryst.

Res. Technol. 36, 837-849.

Sgualdino, G., Aquilano, D., Cincotti, A., Pastero, L. and Vaccari, G. (2006). Face-by-

face growth of sucrose crystals from aqueous solutions in the presence of raffinose. I.

Experiments and kinetic-adsorption model., J. Cryst. Growth. 292, 92-103.

Sgualdino, G., Aquilano, D., Tamburini, E., Vaccari, G. and Mantovani, G. (2000). On

the relations between morphological and structural modifications in sucrose crystals

grown in the presence of tailor-made additives: effects of mono- and

oligosaccharides. Mater Chem Phys. 66,316-322.

58

Sgualdino, G., Aquilano, D., Vaccari, G., Mantovani, G. and Salamone, A. (1998).

Growth morphology of sucrose crystals: The role of glucose and fructose as habit-

modifiers. J. Cryst. Growth. 192, 290-299.

www.freepatentsonline.com/6555544.htm, US Patent, downloaded on July24, 2008.


Kinetics and thermodynamics of sucrose crystal Kinetics and thermodynamics of sucrose crystal Kinetics and thermodynamics of sucrose crystal Kinetics and thermodynamics of sucrose crystal growth growth growth growth

in in in in the the the the presence of a nonpresence of a nonpresence of a nonpresence of a non----ionic surfactant ionic surfactant ionic surfactant ionic surfactant according to a according to a according to a according to a

spiral nucleation modelspiral nucleation modelspiral nucleation modelspiral nucleation model

Abstract

Batch experiments were carried out to study the effect of Hodag CB6, a non-ionic

surfactant, on the growth kinetics of sucrose crystals as a function of supersaturation,

impurity concentration and temperature. The growth promoting effect of the added

impurity, studied using a recently introduced spiral nucleation model (SNM), was due

to the decrease in the surface free energy induced by the added surfactant. The

growth process was influenced by both kinetic and thermodynamic effect, being the

latter effect dominant. The coverage of impurity molecules on the sucrose surface

followed a Henry type expression according to Langmuir isotherm at studied

temperatures. In the case of pure system, the total active kink density was found to be

around 1016 kinks/m2. The active growth sites on the crystal surface were found to be

two orders of magnitude lower than the total number of sucrose molecules.

5.1. Introduction

Impurities in supersaturated solutions will significantly affect the growth rate,

nucleation, morphology, and also the agglomeration rate of the crystals. The kinetics

of crystal growth from aqueous solution is a very complex process, because of the

multiple steps (diffusion and integration) involved. The presence of impurity may

play a significant role in either of these steps (Sangwal, 1999). The presence of

impurities also showed a significant alteration in the morphology of the growing

crystals (Murugakoothan et al., 1999; Sangwal, 1996; Sangwal, 1993). Several works

have been reported dealing with the effect of impurities on the growth and dissolution

kinetics of crystals in solutions. The impurities either increase or decrease the growth

rate of crystals depending on the surface properties of the crystal, impurity and also

on the solute. Some impurities may exhibit selective influence on a particular

crystallographic face. The impurities added to solution with the aim to either alter the

60

growth rate of growing crystals or to modify the crystallographic structure are in

general called as additives. The effects of additives can be classified as

thermodynamic or kinetic (Al-Jibbouri et al., 2002). Many investigations are being

carried out to explain the effect of impurity on the growth kinetics in several

crystallization systems. Most of the literature reports the inhibiting effect of impurity

on the crystal growth kinetics. The inhibiting effect of additives was explained based

on the adsorption of impurity in the kink sites. Growth promoting effect of impurity

was explained for few crystallization systems and was found to be influenced by the

concentration of additives.

In the present study, the surfactant Hodag CB6 increased, globally, the crystal

growth rate of sucrose. For the same supersaturation the growth rate increases with

the impurity concentration, this effect being more pronounced for 30 ºC. The

inhibiting effects of additive or impurity on the growth of crystals are usually

modeled based on the mechanism of impurity sorption in kinks and in terrace

considering the kinetic effects (Al-Jibbouri et al., 2002). The increase in growth rate

was usually modeled considering the thermodynamic effect which is due to the

adsorption of impurity on growing surface leading to decrease in the surface energy

(Kuznetsov et al., 1998). Many investigations are carried out mainly focusing on the

kinetics effects of impurities. Only few studies are dedicated towards the

thermodynamic effects due to the addition of impurities (Kuznetsov et al., 1998;

Sangwal and Brzóska, 2001).

Several kinetic models were used to explain the kinetics and thermodynamic

effects of the impurities on the crystal growth process. Kubota-Mullin (2000) and

Cabrera-Vermilyea (1958) kinetic models are the most used to explain the inhibiting

effect of the impurities on the crystal growth process.

Recently the kinetic effect of added impurity was proposed and explained

based on a competitive sorption model for the growth of sucrose crystals (Martins et

al., 2007). BCF surface diffusion model (Burton et al., 1951; Kumar, 1979), multiple

nucleation model (Kumar, 1979; Sangwal, 1998) and a model involving the complex

source of cooperating dislocations (Chernov et al., 1986; Sangwal, 1998) were found

to be excellent in explaining the kinetic and thermodynamic effects simultaneously. A

review on these kinetics models was made by Sangwal (Sangwal, 1996).

In the present study, the growth promoting effect of Hodag CB6TM on the

kinetics of sucrose crystal growth was studied as a function of supersaturation,

61

temperature and impurity concentration. Hodag CB6 is alpha-methyl glucoside ester,

widely used in sugar crystallization to lower viscosity of sugar by-products (C

massecuite and molasses) and also, by this way, improving the separation of C sugar

in the centrifugals. To the best of our knowledge, no works have been devoted

exclusively studying the effect of this surfactant on the growth of sucrose crystals.

The spiral nucleation model proposed by Martins and Rocha (2007), that incorporates

the features of the two dimensional mechanisms was used to explain the kinetic and

thermodynamic effects of the added impurity on the growth kinetics of sucrose

crystals.

5.2. Experimental

Growth of sucrose crystals was carried out in a 4 L batch agitated crystallizer (Fig.

3.1) at two different temperatures, 30 and 50 ºC. The agitation inside the crystallizer

was maintained at a constant speed of 250 rpm. Crystal growth experiments were

carried out in the presence of surfactant ranging from 0.063 to 0.254 g/L of H2O and

0.0713 to 0.356 g/L of H2O at 30 and 50 oC, respectively. Experiments in the absence

of surfactant were also made. The experiments were carried out for 24 to 72 h,

depending on the solution temperature, until the supersaturation reaches 7 g of

sucrose/100 g of water, approximately. Assuming no spontaneous nucleation and

crystal breakage, the mass of the crystals inside the crystallizer at any time was

calculated from mass balance as explained in section 3.3.

5.3. Results and discussion

Figs. 5.1a and 5.1b show the plots of overall growth rate, Rg, versus

supersaturation,σ , for the range of supersaturation and surfactant concentrations

studied at 30 and 50 oC, respectively. It can be observed that the growth rate of

sucrose crystals was greatly influenced by the added surfactant. Further, the added

surfactant promotes the crystal growth rate increasing it with surfactant concentration.

A similar effect was previously reported for the growth of ammonium oxalate

monohydrate crystals in presence of Fe (III) ions (Sangwal and Brzóska, 2001). The

growth promoting effect can be explained on the basis of reduction in the surface

energy due to the adsorption of surfactant molecules at the kink sites (Sangwal and

Brzóska, 2001; Cabrera and Vermilyea, 1958, Davey, 1976; Tai et al., 1992; Shor and

Larson, 1971). The growth promoting effect due to the added impurity is usually

called as the thermodynamic effect of impurities (Davey, 1976). The decrease in

62

surface free energy increases the step velocity and the increase in step velocity refers

to the kinetic effect and can be studied from the increase in the kinetic constant in the

Fig. 5.1a. Experimental overall growth rate of sucrose crystals for different surfactant concentrations at 30 oC.

case of growth promoting conditions due to impurities. Previously, several studies

have been carried out to explain the inhibiting and promoting effect of impurities on

the growth of crystals using several theoretical models (Davey, 1976; Tai et al., 1992;

Shor and Larson, 1971; Sangwal and Brzóska, 2001; Sangwal, 2008; Kubota, 2001).

Sgualdino et al. (2005, 2006) studied the growth kinetics of several faces of sucrose

crystals in the presence of raffinose. Considerable amount of works are reported

considering the kinetic effect of the impurities on the growth process and only few

studies were made about the thermodynamic effects of the added impurities on the

growth kinetics. Kubota-Mullin (Kubota et al., 2000; Kubota, 2001) and the Cabrera

and Vermilyea (1958) models are the widely used models to explain the growth

inhibition kinetics due to the impurities in solutions. The theoretical models that

incorporate the thermodynamic and kinetic parameters will be useful to study the

effect of thermodynamics and kinetics simultaneously. In the present study, the

63

growth promoting effect of the surfactant, or the thermodynamic effect, and the

kinetic effect were studied simultaneously using the SNM.

Fig. 5.1b. Experimental overall growth rate of sucrose crystals for different surfactant concentrations at 50 oC.

This model combines the concepts of 2D nucleation and BCF model to explain the

growth kinetics of sucrose crystals. The transient kinetic behaviour of the growth

process according to SNM is given by (Martins and Rocha, 2007):

σβπρ1

2

exp2

−=kT

Wvn

y

h

L

Rsp

o

cg (5.1)

where the term1β is a constant and is equal to the height of an elementary step, h.

From the BCF model, the kinetic constant for the growth of crystals, β , is given by:

−=kT

Whvexpβ (5.2)

where v is a frequency factor of the order of atomic vibration frequency, 1013 s-1

(Burton et al., 1951).

Substituting Eq. (5.2) in (5.1), the SNM expression is given by

64

βσπρsp

o

cg ny

h

L

R 22= (5.3)

The density of stable spirals in equilibrium is given by (Burton et al., 1951; Martins

and Rocha, 2007):

∆−=

kT

G

l

yn co

sp exp2

λ (5.4)

The Gibbs energy for the formation of stable nuclei is given by (Martins and Rocha,

2007):

( )σγ

+Ω=∆1ln

64.12

kThGc (5.5)

Combining Eqs. (5.3), (5.4) and (5.5), the SNM can be written as:

( )

+Ω

−=σ

γβλπρσ 1ln

164.1exp

22 h

kTlh

L

Rc

g (5.6)


( ) ( )σγβ

σ +Ω

−=

1ln

164.1lnln

2

hkTL

RSNM

g (5.7)

where Rg/L is the normalized growth rate and the constant, SNMβ , is given by:

βλπρβl

hcSNM2= (5.8)

Thus, the constantSNMβ and the interfacial tension kTγ , assumed constant for the

supersaturation range used, can be determined from the intercept and slope of plot

between

σL

Rgln and ( )σ+1ln1 . Figs. 5.2a and 5.2b show the kinetics of the

sucrose crystal growth process according to linearized SNM expression. Assuming

3/1Ω=h and using 3301004.715 m−×=Ω (Martins and Rocha, 2007), the surface free

energy as a function of surfactant concentration can be obtained from the slopes of the

Figs. 5.2a and 5.2b. From these figures, it can be observed that experimental data fits

very well SNM validating the assumptions behind this model. The calculated

interfacial tensions at 30 and 50 oC were plotted against the surfactant concentration

as shown in Fig. 5.3. It can be observed that, globally, the interfacial tension

decreases with increase in surfactant concentration. This is in agreement with the

65

theory that the increase in growth rate could be due to the decrease in surface free

energy due to the adsorption of impurities at the kink sites.

Fig. 5.2a. Effect of surfactant on the growth kinetics of sucrose crystals at 30 oC, according to SNM.

The results clearly show that the increase in growth rate is due to the thermodynamic

effect of the surfactant, i.e., due to the decrease in surface free energy of the sucrose

crystals.

Assuming the dimension of growth units, h, equal to the height of a

elementary step, the kinetic constant, SNMβ , can be determined from the intercept of

the Figs. 5.2a and 5.2b. Fig. 5.4 shows the calculated kinetic constant SNMβ vs.

surfactant concentration, cs, for the growth experiments at 30 and 50 oC. It can be

observed that the constant SNMβ , globally, decreases with increase in surfactant

concentration. The value of SNMβ for pure solution at 30 ºC is clearly underestimated,

66

this being due to a higher scattering of data for those conditions. The variation of

SNMβ with surfactant concentration is due to the variation in kinetic coefficient, β , or

otherwise the activation energy W for growth according to Eq. (5.2).

Fig. 5.2b. Effect of surfactant on the growth kinetics of sucrose crystals at 50 oC, according to SNM.

From the values of SNMβ andγ , Figs. 5.4 and 5.3, it could be concluded that the

increase in the growth rate in the presence of surfactant is due to the decrease in the

free energy of the surface following the adsorption of surfactant on the kink sites. The

decrease in both SNMβ and γ clearly indicates the combined effect due to the

thermodynamics and kinetics with increase in surfactant concentration at the studied

temperatures. A similar effect was previously reported for the growth of 001 face of

ammonium oxalate monohydrate in presence of Cu(II) ions (Sangwal and Brzóska,

2001). The increase in growth rate with impurity concentration suggests the

domination of thermodynamic effect more than the kinetic effect of Hodag CB6 on

the growth kinetics of sucrose crystals.

67

Representing the surface free energy of pure sucrose crystal by oγ , the rate of

decrease in the surface energy with respect to the added surfactant fits the empirical

relation, as shown in Fig. 5.5

)1( Sio ck−= γγ (5.9)

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0.0022

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

cs, g/L

γγ γγ, J

/m2

30 ºC

50 ºC

Fig. 5.3. Effect of surfactant concentration on the surface free energy,γ , at 30 and 50 oC.

The assumed value for the surface energy, oγ , at 30 ºC was obtained considering the

equation that best fits the other experimental points, taking into account what was

already said about the insufficient accuracy of the correspondent experimental value.

By this way, γ for pure system at 30 ºC was found to be 2.20 x 10-3 J/m2.

Eq. (5.9) can be transformed in:

( ) ( ) ( )Sio ck

kT

h

kT

h −Ω

=Ω1

2/12/1 γγ (5.10)

The physical meaning of the last two equations could be interpreted by rewriting the

linearized SNM expression introducing the free energy change for the formation of

68

stable nuclei, and using an approach previously reported to explain the growth

promoting effect of Fe(III) ions on ammonium oxalate monohydrate crystals

(Sangwal, M.E. Brzóska, 2001).

( ))1ln(

1)1ln(lnln

σσβ

σ +

+∆−=

kT

G

L

Rc

SNMg (5.11)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

cs, g/L

ββ ββSN

M,

kg/m

3 s

30 ºC

50 ºC

Fig. 5.4. Plot of SNM kinetic constant, β SNM, versus surfactant concentration, cs, at 30 and 50 oC

Introducing the term F defined by

+∆=

kT

GF c )1ln( σ

(5.12)

and writing the term F in Eq. (5.12) in terms of the surface free energy, γ , i.e.,

( ) ( ) 2/121 64.1/FkTh =Ωγ , then, for 1»kicS, an expression analogous to Eq. (5.10),

relating the free energy change with respect to added surfactant, can be written as

69

( )Sicoc ckGG −∆=∆ 1 (5.13)

where coG∆ represents the value of cG∆ when cS = 0.

According to Eq. (5.13), the free energy change, cG∆ , decreases with increase in

impurity concentration. The rate of nucleation of solution can be affected

considerably by the presence of impurities in the system. The presence of impurity

can induce the nucleation at degrees of super cooling less than that required for

spontaneous nucleation (Mullin, 1993). Eq. (5.13) is in analogy with the classical

nucleation theory, i.e., the overall free energy required for the formation of critical

nucleus under heterogeneous condition, DhetG 2*∆ , must be less than the corresponding

free energy associated with homogeneous nucleation, hom2* DG∆ , i.e (Mullin, 1993):

hom22 ** DDhet GG ∆=∆ φ (5.14)

where, φ is less than unity.

Eq. (5.14) is similar to the Shishkovskii’s empirical expression (Sangwal and

Brzóska, 2001):

( )]1ln1[ θγγ −−= Bo (5.14)

Where, θ is the surface coverage of the impurity, and B is a constant given by:

mo

kTB

ωγ= (5.15)

where mω is the surface area per adsorbed molecule and lies between 0.2-0.4 nm2. For

low impurity concentrations, ln( ) SLcK==− θθ1 , and in this case Eq. (5.15) can be

written as (Sangwal and Brzóska, 2001):

]1[ SLo cBK−= γγ (5.17)

where, KL is the Langmuir constant given by (Sangwal and Brzóska, 2001):

=

RT

QK diff

L exp (5.18)

R is the gas constant and Qdiff is the differential heat of adsorption of the impurity on

the surface.

Fig. 5.5 shows the plot between oγγ / and cS at 30 and 50 oC. According to

Shiskovskii’s empirical expression, the Langmuir constant, KL, can be determined

from slope of Fig. 5.5 using Eqs. (5.16) and (5.17). The KL value was found to be

70

0.230 L/g and 0.070 L/g at 30 and 50 oC respectively. Assuming the isotherm follows

a Shishkovskii isotherm, the surface coverage, θ, can be predicted from θ=KLcS.

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

cs, g/L

γ/γ

o

30 ºC

50 ºC

Fig. 5.5. Shishkovskii’s plot for Hodag CB6 onto sucrose surfaces at 30 and 50 oC

The KL value can be used to determine the Gibbs free energy and other

thermodynamic parameters using Eqs. (5.19) to (5.21) (Gupta and Rastogi, 2008):

( )LKRTG ln−=∆ (5.19)

−∆−=

12

2 11ln

1TTR

H

K

K

TL

TL (5.20)

STHG ∆−∆=∆ . (5.21)

In the present study, the molecular weight of the surfactant used was assumed to be

14,000. Molecular weight of 14,000 was assumed from the value of molecular weight

of PluronicTM F 108 which has a similar composition to that of HodagTM Non-ionic

(www.freepatentsonline.com/6555544.htm, US Patent). This was made since the

information about the molecular weight was not readily available or provided.

71

However, the KL values reported in terms of L/g can be used at any time to recalculate

the thermodynamic parameters if the molecular weight of the surfactant is available.

So, the calculatedG∆ for the sorption of surfactant molecules onto the sucrose

surface at 30 and 50 oC was found to be -20.4 kJ/mol and -18.5 kJ/mol, respectively.

The H∆ and S∆ for the sorption of surfactant molecules onto the sucrose surface

were estimated as -48.1 kJ/mol and -91.5 J/mol respectively. The negative H∆ value

shows that the sorption of surfactant molecules onto the sucrose surface is an

exothermic process. The decrease in G∆ with increasing temperature suggests that

the decrease in the surface free energy with respect to added surfactant was more

evident at lower temperature.

The step kinetic coefficient for the growth of crystals for different

concentrations of surfactant was calculated using Eq. (5.2). The growth of crystals

occurs at the specific active surface sites where dislocations emerge from the crystal.

Dislocations found in crystals can be of edge or screw dislocations or can have any

degree of mixed type, however only screw dislocations are responsible for generating

the growth steps (Shiau, 2003). In this study the total number of dislocations per m2,

λ , was assumed to be 1016. This is the typical value of the kink density determined

from this study, and it was assumed that λ is not much far away from this value. From

λ and assuming equal the distance between steps (later calculated) and the average

distance between the dislocations, the kinetic constant, β, can be related with the

constant βSNM as:

ββ 81047.8 ×=SNM (5.22)

Combining Eqs. (5.2) and (5.22), the kinetic constant, β, was used to calculate the

activation energy, W, for the growth of sucrose crystals according to spiral nucleation

model (given in Table 5.1). The activation energies for the step growth were found to

be in the range of 71.7 to 77.3 kJ/mol for the studied experimental conditions.

Previously, Bennema (1968) determined that the activation energy using the BCF

model for the surface reaction of sucrose crystals is between 65.7 and 69.9 kJ/mol.

Recently Shiau (2003) reported the activation energy for sucrose crystals using BCF

theory as 66.6 kJ/mol. Thus, and taking into account the simplifying assumption used,

the activation energy calculated using SNM was found to be in close agreement with

the values reported by Bennema (1968) and Shiau (2003). The obtained activation

72

energies further suggest that the growth of sucrose crystals for the studied conditions

was surface integration controlled (Mullin, 1993).

In addition to the thermodynamic parameters, the determined surface free energy

using the spiral nucleation model can be used to calculate several topological

Table 5.1. Activation energy for sucrose growth according to SNM.

Temperature: 30 oC Temperature: 50 oC cs, g/L of

water Activation energy,

W (kJ/mol) cs, g/L of

water Activation energy,

W (kJ/mol) 0 73.8 0 76.0

0.063 71.7 0.071 76.1 0.127 72.6 0.142 76.0 0.190 72.7 0.213 77.2 0.254 73.9 0.285 77.3

0.356 77.3

parameters such as the kink distance, the step distance of a growth spiral, the distance

between two neighbor steps of spirals and the kink density of the crystal surfaces. The

expressions for determining topological parameters are given and elaborated by

Nielsen (1981). For a fixed supersaturation, the mean distance between two

neighboring kinks of a spiral step, xo, and the critical radius of the 2D nucleus can be

calculated using Eqs. (5.23) and (5.24), respectively (Budevski et al., 1975).

= −

kTdSx ed

o

γexp2/1 (5.23)

( )SkT

ar ed

ln*

γ= (5.24)

where, edγ is the free edge work given by 2ded γγ = , and d is the diameter of the crystal

growth unit.

The distance between consecutive turns of the spiral, yo, was given by BCF and later

revised by Cabrera and Levine (1956) and Budevski et al. (Budevski et al, 1975).

*19ryo = (5.25)

The density of kinks on the surface of growing crystal with rate controlled by a spiral

mechanism is given by (Christoffersen and Christoffersen, 1988):

( )( ) ( )kTkTa

SS

yx ededoo /exp/19

ln12

2/1

γγ= (5.26)

73

At 30 oC, for a pure system at a supersaturation, σ , of 0.0738, xo, r*, yo and 1/xoyo

values were found to be 1.08 x 10-9, 2.47 x 10-9, 4.69 x 10-8 m and 1.97 x 1016

kinks/m2, respectively. For the growth of pure sucrose crystals at 50 oC for σ =0.088,

xo, r*, yo and 1/xoyo values were found to be 1.19 x 10-9, 3.41 x 10-9, 6.48 x 10-8 m and

1.29 x 1016 kinks/m2, respectively.

Assuming that the height of the spiral step is equal to the height of unit cell,

the mean rate of advancement of steps is given by 3/1ΩR . The 3/1ΩR value for the

growth of pure sucrose crystals was found to be 8.31 x 109 and 2.02 x 1010 crystal

monolayers/sec at 30 and 50 oC, respectively. The molecules of sucrose on the crystal

surface can be calculated from the area occupied by one sucrose molecule which is

equal to the projection on the surface. The area occupied by one sucrose molecule is

given by (Koutsopoulos, 2001):

3/2Ω=sucroseA (5.27)

Assuming that the area occupied by one molecule is equal to its projection on

the surface, the moles of sucrose molecules on the crystal surface, Css, can be

calculated using Eq. (5.27) and was found to be 1.25 x 1018 molecules/m2. Comparing

the Css with the kink density (1.29 x 1016 kinks/m2) of sucrose molecules, it can be

observed that the active growth sites on the crystal surface was found to be 2 order of

magnitude less than the total number of sucrose molecules. A similar observation was

previously reported during the growth of hydroxyapatite (HAP) crystals

(Koutsopoulos, 2001). In the case of growth of HAP crystals, the active kink sites

were found to be four times lower than the total density of the kinks on the crystal

surface. This mechanistic approach was found to be useful in identifying the number

of active sites that are involved in the crystal growth process. In addition, using the

calculated surface energy coming out from the BCF model, the effect of the surface

energy due to the addition of impurity on 1/xoyo can be predicted. In the present case,

at the studied temperatures, only a part of kink sites are actively involved in the

growth process and the most of them do not contribute for the crystal growth process

as they are located on the flat crystal area between the steps and spirals

(Koutsopoulos, 2001).

5.4. Conclusions

The growth promoting effect of Hodag CB6, a non-ionic surfactant, on the kinetics of

sucrose crystals in solution was explained using a recently introduced spiral

74

nucleation model (SNM). The SNM was found to be successful in representing the

kinetics of sucrose crystal growth process for the range of surfactant concentrations

and temperatures studied. The growth process was influenced by both the kinetic

growth inhibition effect and the thermodynamic effect, the latter being preponderant

for the range of surfactant concentration studied. The growth promoting effect was

due to decrease in the surface free energy induced by the addition of surfactant. The

surface free energy determined by SNM was found to decrease with increasing

surfactant concentration. The coverage of impurity molecules on the sucrose surface

follows a Henry type expression according to a Langmuir isotherm at 30 and 50 oC.

The active growth sites on the crystal surface was estimated and was found to be two

orders of magnitude lower than the total number of sucrose molecules.

75

5.5. References



Bennema, P. (1968). Surface diffusion and the growth of sucrose crystals. J. Cryst.

Growth. 3-4, 331-334.

Bubnik, Z. and Kadlec, P. (1992). Sucrose crystal shape factor. Zuckerindindustrie.

117, 345-350.

Budevski, E., Staikov, G. and Bostanov, V. (1975). Form and step distance of

polygonized growth spirals. J. Cryst. Growth. 29, 316-320.


equilibrium structure of their surfaces. Phil. Trans. Roy. Soc. London. 243, 299-

358.

Cabrera, N. and Levine, M.M. (1956). On the dislocation theory of evaporation of

crystals. Philos. Mag. 1-5, 450-458.

Cabrera, N. and Vermilyea, D.A. in: R.H. Domeus, B.W. Roberts, D. Turnbull,

(Eds.), Growth and perfection of crystals, Wiley, New York, 1958, p.393.

Chernov, A.A., Rashkovich, L.N. and Mkrtchan, A.A. (1986). Solution growth

kinetics and mechanism: Prismatic face of ADP., J. Cryst. Growth. 174, 101-112.

Christoffersen, J. and Christoffersen, M.R. (1988). Spiral growth and dissolution

models with rate constants related to the frequency of partial dehydration of

cations and to the surface tension. J. Cryst. Growth. 87, 41-50.

Davey, R.J. (1976) The effect of impurity adsorption on the kinetics of crystal growth

from solution, J. Cryst. Growth 34. 109-119

Guimaraes, L., Sa, S., Bento, L.S.M. and Rocha, F. (1995). Investigation of crystal

growth in a laboratory fluidized bed, Int. Sugar J. 97, 199-204.

Gupta, V.K. and Rastogi, A. (2008). Equilibrium and kinetic modelling of

cadmium(II) biosorption by nonliving algal biomass Oedogonium sp. from

aqueous phase. J. Hazard. Mater. 153, 759-766.


Langmuir 17, 8092-8097.


Technol. 36, 8-10.

76


supersaturation and impurity concentration on crystal growth. J. Cryst. Growth.

212, 480-488.

Kumar, C. (1979). A new look at the BCF surface diffusion model. J. Cryst. Growth.

48, 489-490.



193, 164-173.


nucleation model. Surf. Sci. 601 (2007) 3400-3408.


kinetics according to a competitive adsorption model. Cryst. Growth Des. 6(12),

2814-2821.

Mullin, J.W. Crystallization, (1993), Third edition, Butterworth-Heinemann, Great

Britain.


Ramasamy, P. (1999). Habit modification of potassium acid phthalate (KAP)

single crystals by impurities., J. Cryst. Growth. 207, 325-329.

Nielsen, A.N. (1981). Theory of electrolyte crystal growth. Pure Appl. Chem. 53,

2025-2039.

Sangwal, K. (1999). Kinetic effects of impurities on the growth of single crystals from

solutions. J. Cryst. Growth. 203 (1999) 197-212.

Sangwal, K. (1996). Effects of impurities on crystal growth processes, Prog. Cryst.

Growth Charact. Mater. 32 (1996) 3-43.

Sangwal, K. (1993). Effect of impurities on the processes of crystal growth, J. Cryst.

Growth. 28, 1236-1244.

Sangwal, K. (1998). Growth kinetics and surface morphology of crystals grown from

solutions: Recent observations and their interpretations. Prog. Cryst. Growth

Charact. Mater. 36, 163-248.


applications, John Wiley & Sons, Ltd.

Sangwal, K. and Brzóska, E.M. (2001a). Effect of Fe(III) ions on the growth kinetics

of ammonium oxalate monohydrate crystals from aqueous solutions. J. Cryst.

Growth 233, 343-354.

77

Sangwal, K. and Brzóska, M.E. (2001b). On the effect of Cu(II) impurity on the

growth kinetics of ammonium oxalate monohydrate crystals from aqueous

solutions. Cryst. Res. Technol. 36, 837-849.

Shor, S.M. and Larson, M.A. (1971). Effect of additives on crystallization kinetics,

Chem. Eng. Progr. Symp. 110, 32-42.

Sgualdino, G., Aquilano, D., Fioravanti, R., Vaccari, G. and Pastero, L. (2005).

Growth kinetics, adsorption and morphology of sucrose crystals from aqueous

solutions in the presence of raffinose. Cryst. Res. Technol. 40, 1087-1093.

Sgualdino, G., Aquilano, D., Cincotti, A., Pastero, L. and Vaccari, G. (2006). Face-

by-face growth of sucrose crystals from aqueous solutions in the presence of

raffinose. I. Experiments and kinetic-adsorption model., J. Cryst. Growth. 292, 92-

103.

Shiau, L.D. (2003). The distribution of dislocation activities among crystals in

sucrose crystallization, Chem. Eng. Sci. 58 (2003) 5299-5304.

Tai, C.Y., Wu, J.F. and Rousseau, R.W. (1992). Interfacial supersaturation, secondary

nucleation, and crystal growth., J. Cryst. Growth. 116, 294-306.

www.freepatentsonline.com/6555544.htm, US Patent, accessed on July24, 2008.


On theOn theOn theOn the effect of a noneffect of a noneffect of a noneffect of a non----ionic surfactant on the surface of ionic surfactant on the surface of ionic surfactant on the surface of ionic surfactant on the surface of

sucrose crystals and on the crystal growth process by sucrose crystals and on the crystal growth process by sucrose crystals and on the crystal growth process by sucrose crystals and on the crystal growth process by

inverse gas chromatographyinverse gas chromatographyinverse gas chromatographyinverse gas chromatography

Abstract

The effect of Hodag CB6, a widely used non-ionic surfactant in sugar crystallization

process, on the surface properties of sucrose was studied in detail by inverse gas

chromatography (IGC) experiments. IGC experiments were performed with pure sucrose

crystals, surfactant coated sucrose crystals, and crystals grown in the presence of

surfactant at 313.05 and 323.05 K. The surfactant promotes the specific interactions with

the polar probes. The sorption of basic, acidic and amphoteric probes onto pure and

surfactant coated sucrose was found to be endothermic and in the case of neutral probes

was found to be exothermic. The surfactant increases both the acidity and basicity of the

sucrose surface with the latter effect being significant. The role of interfacial tension on

the growth kinetics of sucrose crystals was studied using IGC for different surfactant

concentrations. IGC results with the surfactant coated sucrose were used to interpret the

thermodynamic effect of surfactants during the crystal growth process. The dispersive

component of the surface energy, Dsγ , of surfactant coated sucrose crystals was found to

be lower than that of pure sucrose crystals and was found to be in the range of 33.49 to

35.27 mJ/m2.

6.1. Introduction

Interfacial tension plays an important role during the growth of crystals in pure and

impure solutions. The crystal growth rate in solution increases with decrease in interfacial

tension which is directly related with the surface energy of the growing crystals (Davey,

1976; Sangwal, 1993). The interfacial tension can be regulated by the addition of

surfactants which adsorb onto the surface of crystals during the crystal growth process. In

80

the case of sucrose crystal growth process, several emulsifiers are used in industrial

processes to regulate the fluidity of the mixture, which in turn affects the growth of

sucrose crystals in solution. The surface properties of sucrose crystals have to be

controlled in order to obtain the desired fluidity (Rousset et al., 2002). Thus, it would be

important to characterize the influence of the emulsifier on the surface properties of the

sucrose. The surface energy can be related to adhesion properties and to the growth

kinetics of sucrose crystals.

According to Fowkes (1980), the surface energy is divided into two components

namely the polar (γp) and dispersive (γD). When a solid comes in contact with the liquid,

an interfacial energy will be created which will depend on the individual surface energies

of the two components. The adsorption of solute onto the surface of solid will be

influenced by the magnitude of the surface free energy.

Different techniques are available for determining the solid surface properties.

These include the Whilmey plate, contact angle method and maximum bubble pressure

techniques. Currently, inverse gas chromatography was found to be a successful tool to

measure the physico-chemical properties. IGC has been used to determine the adsorption

thermodynamics and surface properties of carbon fibre-epoxy composites (Schultz et al.,

1987), polycarbonates (Panzer and Schreiber, 1992), cellulose fibers (Balard et al., 2000),

polymers (Wu et al., 2007), brich wood meal (Kamdem et al., 1993), activated carbons

(Garzon et al., 1993), kaolinites and illites (Saada et al., 1995), hemp fibers (Gulati and

Sain, 2006) and RDX (Luo and Du, 2007). IGC technique was also widely used to study

the surface properties of pharmaceutical powders (Grimsey et al, 2002), to study the acid-

base characteristics of lignocellulosic surfaces (Tshabala, 1997). A review on the

applicability of IGC technique for the examination of physiochemical properties of

various materials and a review about IGC technique in characterizing specifically the

porous materials were recently made by Voelkel et al (2009) and Thielmann (2004),

respectively. Previously, IGC was also used to study the surface properties of sucrose

coated with lecithin (Rousset et al, 2002).

In the present study IGC was used to characterize the surface properties of` the

sucrose and the sucrose coated with surfactant (Hodag 6B). Two types of samples,

sucrose coated with surfactant and sucrose from the crystal growth experiments in

81

presence of surfactant were analyzed using IGC. Retention time of polar and apolar

probes were employed to determine the effect of emulsifier on the dispersive surface

energy, acid-base parameters and adsorption thermodynamics.

6.2. Experimental

6.2.1. Crystal growth experiments

Growth of sucrose crystals was made in a 4 L batch agitated crystallizer at 30 oC. The

agitation inside the crystallizer was maintained at a constant speed of 250 RPM. Sucrose

solutions were prepared by dissolving the sucrose crystals at 50oC in ultra pure water. In

all cases the surfactant was added while dissolving the sucrose at 50oC. Supersaturation

was obtained by cooling down the solution to working temperature. All the experiments

were carried out for an initial supersaturation of 20 g of sucrose/100 g of water. Once the

crystallizer temperature was stable, an accurately weighed amount of 16 g of sucrose seed

crystals was added into the crystallizer. Crystals ranging within the sieve fractions 0.0425

to 0.0500 cm were used as seed crystals. In the present study, crystal growth experiments

were carried out with surfactant concentration ranging from 0.0635 to 0.1271 g/L of

water, until a supersaturation value of roughly 7 g of sucrose/100 g of water. The mass of

the crystals inside the crystallizer at any time was calculated by mass balance.

6.2.2. Sucrose sample preparation

The surface of sucrose crystals was coated with surfactant by dispersing the crystals in

the hexane containing emulsifier in a proportion of 50% (w/w) sucrose powder, 50%

(w/w) hexane and 2% (w/w) Hodag CB6. Surfactant was added in excess to ensure the

complete coverage of the sucrose surfaces. The suspension was kept under agitation for

24 hours at 20 oC. The solution was filtered and the filtrate was washed with hexane for

three times to remove the excess surfactant. The remaining surfactant was removed by

placing the sample in a vacuum oven for 48 h at 40 oC and 40 mbar.

6.2.3. IGC experiments

IGC measurements were carried out in duplicate using a commercial inverse gas

chromatograph (Surface Measurements Systems, London, UK) equipped with flame

ionization (FID) and thermal conductivity (TCD) detectors. Standard glass silanized

(dimehyldichlorosilane; Replicote BDH, UK) columns with 0.4 cm inner diameter and 30

82

cm length were used. About 3 g of sample were weighed for the analysis. Samples were

packed by vertical tapping for 220 min. The columns with the samples were conditioned

overnight at 323.05 K and 10 ml/min of flow rate (helium) to remove the impurities

adsorbed on the surface. The pressure drop on the column at the flow rate of He of

10mL/min at 100 oC was 2.5 kPa. After pre-treatment, pulse injections were carried out

with a 0.25 mL gas loop.

The IGC setup with a head space injection facility used in the present study is

shown in Fig. 6.1. The carrier gas (helium) is passed through a reservoir containing the

probe molecule in its liquid form, where the carrier gas is saturated with the probe

molecule and then flowing through the injection loop. The headspace injection system

Fig. 6.1. Schematic diagram of the IGC experimental set-up used in this study with head-space injections (For more details readers are suggested to check in the manufacturer website: http://www.thesorptionsolution.com/Products_IGC.php).

helps to potentially deliver more reproducible injection volumes (Thielmann, 2004).

Concentration and the amount of probe molecule are controlled via the temperature and

FID/TCD

Hood

Vapour generation

Carrier gas

Loop

Column

Sample column oven

83

the loop volume (in this study 0.25 µL). The instrument used in the present study has a

number of innovative design futures including the ability to use up to ten different gas

probe molecules in any one experiment and the ability to condition the sample under a

wide range of humidity and temperature conditions. A separate sample column oven as in

Fig. 6.1 allows the sample to be studied over a wide range of temperatures. The retention

time was calculated from the FID response for the subsequent injections of probe

molecules. The iGC system is highly advanced and fully automatic with SMS iGC

Controller v1.3 control software.

0

2000

4000

6000

8000

10000

12000

0.4 0.9 1.4 1.9 2.4 2.9

Retention time, min

FID

Res

po

nse

(p

A)

Nonane

Decane

Undecane

04000080000

120000160000

0.2 0.3 0.4 0.5 0.6

Methane

Fig. 6.2. Experimental elution profiles of nonane, decane, undecane and methane for the column packed with pure sucrose crystals at 50 oC.

84

Measurements of dispersive interactions were made with n-alkanes (n-heptane, n-

octane, n-decane and n-undecane) at 313.05 K and 323.05 K at 0% RH (relative

humidity) at a flow rate of 10 ml/min. For acid-base and Gibbs free energy studies

acetonitrile, ethyl acetate, acetone and dichloromethane were used at 0% RH. A typical

response of FID to the injection of nonane, decane, undecane at 323.05 K is shown in

Fig. 6.2 for reference. Fig. 6.2 also encloses the FID response for the tracer (methane)

molecule which was used to calculate the dead-time of the column filled with pure

sucrose crystals. The gross and dead time can be calculated from the FID response. The

retention volume can be easily determined from the gross and dead time using Eq. (6.2)

explained in the later sections.

6.3. Results and Discussion

The surface energy can be attributed to the dispersive component arising from London,

van der Waals and Lifshitz forces (Fowkes, 1980) and the acid/base component arising

from both Lewis acid/base interactions and hydrogen bonding (Gutmann, 1978). The

retention time of a series of homologous alkanes which are neutral liquids was used to

determine the dispersive surface free energy of the sucrose samples. The dispersive

component of the pure and the surfactant coated sucrose crystals was obtained from the

Schultz et al (1987) expression:

( ) ( ) caNVRT DL

DsN += 5.05.0

2ln γγ (6.1)

where VN is the net retention volume, Dsγ is the dispersive solid surface energy, DLγ is the

dispersive liquid surface energy, N is the Avogadro number, a is the area of surface

occupied by a molecule of vapor probe and c is a constant. The retention volume can be

obtained by subtracting the holdup volume from the solute total elution volume.

Assuming the alkane probes have no acid/character and thus interact with the

surfaces only by dispersive forces, Dsγ can be calculated from the slope of NVRT ln

versus ( ) 5.0DLaN γ for a homologous series of hydrocarbons using Eq. (6.1).

The net retention volume in Eq. (6.1) can be calculated using (Thielmann, 2004):

( )m

jwtt

T

TV os

rN −= (6.2)

85

where w is the exit flow rate measured at 1atm and room temperature, m is the sample

mass, T is the column temperature, Tr is the room temperature, ts is the retention time of

the probe liquids, to is the dead time (mobile phase hold-up time) and j is the James-

Martin pressure drop correction factor, which corrects the retention time for the pressure

drop in the column bed and is given by (Thielmann, 2004)

( )( ) 1/

1/5.1

3

2

−−

=oi

oi

PP

PPj (6.3)

Where Pi is the inlet pressure of the carrier gas, and Po is the outlet pressure of the carrier

gas, which is usually equal to the atmospheric pressure

From the concepts of Drago (1977), Gutmann (1978) and Fowkes (1980) the non-

dispersive or specific interactions are due to acid-base or electron acceptor-donor

interactions and the strong interactions can develop only between an acid and a base.

According to Gutmann (1978) acid-base concept, a Lewis base is an electron pair donor

(EPD) characterized by donor number DN and a Lewis acid is an electron pair acceptor

(EPA) characterized by the acceptor number AN. In the present study nine probes

exhibiting neutral, basic, acidic and amphoteric characteristics were used to characterize

the surface properties of sucrose samples. The characteristics of the probes used are given

in Table 6.1. The surface area of the probe molecules and the dispersive liquid surface

energy were determined by injecting the probes on neutral reference solids and by contact

angle method on reference solids respectively. The Gutmann’s DN and AN numbers are

taken from literatures.

When polar probes are used as adsorbates both dispersive and specific interactions

take place and thus the Gibbs free energy of adsorption, oadsG∆ , is decomposed into two

components, dispersive DadsG∆ and specific, spe

adsG∆ which are considered to be

independent as shown below (Rousset et al., 2002):

spads

Dadsads GGG ∆+∆=∆ 0 (6.4)

In the present study, to determine the specific surface interactions it is presumed that the

assumption of Schultz et al. (1987) holds true, i.e., the specific interactions are simply

added to the dispersive interactions. With this assumption, the trend line between

NVRT ln versus ( ) 5.0DLNa γ for polar probes will lie above the trend line corresponding to

86

homologous series of n-alkanes. Thus, the specific free energy spadsG∆ for the interaction

between the polar probe and the sucrose surface can be obtained from the difference

between the ordinates of n-alkane line and the corresponding polar probe as (Schultz et

al, 1987; Saada et al, 1995):

alkanesnNpolarNspads VRTVRTG −−=∆ ,, lnln (6.5)

VN,polar and VN,n-alkanes are the retention volume of the polar probe and retention volume of

n-alkanes, respectively.

Using the Saint-Flour and Papirer (Flour and Papirer, 1983) expression, the polar

characteristics of the sucrose surface can be predicted from the enthalpy of adsorption,

∆H:

BA

spads K

AN

DNK

AN

H+=

∆. (6.6)

Riddle and Fowkes (1990) reported the corrected Gutmann’s acceptor number, AN*,

considering the dispersion effect. Riddle and Fowkes related the AN* with the original

AN numbers by the equation

AN* = 0.288(AN-ANd) (6.7)

Thus Eq. (6.6) is given by:

BA

spads K

AN

DNK

AN

H+=

∆*

.*

(6.8)

Estimation of KB from the intercept of Eq. (6.8) may lead to the significant error, thus the

KB was calculated from the slope of the following expression

AB

spads K

DN

ANK

DN

H+=

∆ *. (6.9)

Recently Voelkel (1991) and Cava et al. (2007) explained an alternate method to

determine the temperature dependent KA and KB values by rewriting Eq. (6.9) in terms of

specific free energy of adsorption

BA

spads K

AN

DNK

AN

G+=

∆*

.*

(6.10)

87

Table 6.1. Characteristics of the probes used in this study (Gutmann, 1978; Drago and Wayland, 1977; Yang et al., 2008; Flour and Papirer, 1983; Riddle and Fowkes, 1990; Lavielle et al., 1991; Schultz et al., 1987; Dong et al., 1989).

Adsorbate

Surface Tension

(J/m²)

Cross Sectional Area

x 1019 (m²)

DN

(J.mol-1)

AN*

(J.mol-1)

Specific

character

Heptane 0.0203 5.73 -- -- Neutral

Octane 0.0213 6.3 -- -- Neutral

Nonane 0.0227 6.9 -- -- Neutral

Decane 0.0234 7.5 -- -- Neutral

Undecane 0.0246 8.1 -- -- Neutral

Acetonitrile 0.0275 2.14 59022.6 19674.2 Basic

Ethyl acetate 0.0196 3.3 71580.6 6279 Basic

Acetone 0.0165 3.4 71162 10465 Amphoteric

Dichloromethane 0.0245 2.45 12558 56511 Acid

88

KA and KB can be calculated from the plot of *ANG sp

ads∆ versus */ ANDN .

Determination of KA and KB using Eq. (6.10) leads to temperature dependent values

containing also entropic factor and thus should not be compared with the values

determined from Eq. (6.8) (Voelkel et al., 2009) (they will be similar if assuming

negligible the entropic contribution).

Figs. 6.3a and 6.3b show the plot of NVRT ln versus ( ) 5.0DLNa γ for a homologous

series of hydrocarbons onto pure sucrose particles and surfactant coated sucrose particles

at 313.05 and 323.05 K, respectively.

Fig. 6.3a. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of n-alkanes onto pure

sucrose crystals.

89

Fig. 6.3b. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of n-alkanes onto

surfactant coated sucrose crystals

The calculated Dsγ values are given in Table 6.2. From Table 6.2, it can be observed that

Dsγ for the surfactant coated sucrose is lower when compared to the pure sucrose surface

at 323.05 K. The decrease in surface dispersive energy may be due to the adsorption of

the surfactant molecules at the crystal surface during the coating process thereby reducing

the Dsγ value. At 313.05 K, D

sγ of the surfactant coated sucrose surface was found to be

higher than in the case of pure sucrose surface. However while considering the

experimental error (based on the values of standard deviation), the change in Dsγ due to

the surface coating was almost negligible at this temperature. These observations show

the importance of temperature and the added surfactant on the role of surface energetics.

Previously, an increase in dispersive surface energy was observed in the case of

90

granulated sucrose coated with lecithin and a decrease in Dsγ was reported for jet milled

sucrose coated with lecithin (Rousset et al., 2002). The dispersive surface energy of the

surfactant coated sucrose was found to decrease with increase in temperature. In the case

of pure sucrose crystals, the dispersive surface energy shows a slight increase with

increase in temperature.

However this value is within the experimental error and could be considered

negligible. This decrease in surface energy is attributed due to an entropic contribution to

the Gibbs free energy with increasing temperature. The pure sucrose being more ordered

than a coated sucrose crystal may have less entropic dependence on the temperature than

a coated sucrose crystal.

Figs. 6.4a and 6.4b show the plot of NVRT ln versus ( ) 5.0DLNa γ for four polar probes and

the adsorption energy of n-alkanes onto pure sucrose crystals and surfactant coated

sucrose crystals at 313.05 K, respectively. The specific free energy of adsorption,

spadsG∆ ,of the pure sucrose and surfactant coated sucrose were calculated using the

difference between the adsorption energy of the polar probe and its dispersive increment,

as shown in Figs. 6.4a and 6.4b, according to Eq. (6.5), and are given in Table 6.2. Table

6.2 also shows the calculated spadsG∆ of the pure sucrose and the surfactant coated sucrose

at 323.05 K. The higher spadsG∆ for the surfactant coated sucrose clearly indicates that

surfactant creates new active sites for specific interactions. The calculated spadsG∆ was

used to predict KA and KB using Eq. (6.10). Figs. 6.5a and 6.5b show the plot of

*ANG sp

ads∆ versus */ ANDN for the pure sucrose and surfactant coated sucrose at

313.05 and 323.05 K, respectively. The linearity of the plots with r2 values in the range of

0.91 to 0.94 suggests (Figs. 6.5a and 6.5b) that the Gutmann’s acid-base concept is valid

for the studied system and the specific interactions may be considered due to electron

donor-acceptor interactions (Panzer and Schreiber, 1992). The calculated KA and KB

values are given in Table 6.2. KA and KB show the acidic and amphoteric characteristics

of the sucrose surface at 313.05 K and 323.05 K respectively. Both KA and KB values

were found to increase with increase in IGC temperature in the case of pure and

surfactant coated sucrose and in both the cases the changes were small.

91

Fig. 6.4a. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of polar probes onto

pure sucrose at 313.05 K.

A similar increase in KA and KB values with IGC temperature was reported for

polycaprolactone and polylactic acid (Kamdem et al., 1993). The KB/KA values of 1.402

and 1.337 in the case of surfactant coated sucrose at 313.05 K and 323.05 K, respectively,

suggest that coating of surface increased the basicity of the sucrose surface significantly.

The KB/KA values for pure and surfactant coated sucrose at 313.05 K indicate the strong

electron acceptor and donor capacity of the pure sucrose and surfactant coated sucrose

crystals.

92

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

12000

0 2E-20 4E-20 6E-20 8E-20 1E-19 1.2E-19 1.4E-19

aN(γγγγLD)0.5, m2(J/m2)0.5

RT

ln(V

N),

J/m

ol

n-alkanes

Acetonitrile

Ethyl acetate

Acetone

Dichloromethane

Fig. 6.4b. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of polar probes onto

surfactant coated sucrose at 313.05 K Table 6.2: γγγγs

D, spadsG∆ , KA and KB for polar and n-alkanes onto pure and surfactant

coated sucrose particles at 313.05 and 323.05 K Pure sucrose Surfactant coated sucrose

Parameter 313.05 K 323.05 K 313.05 K 323.05 K

∆Gacetonitrile (kJ/mol) 5.48 + 0.13 6.61 + 0.09 9.11 + 0.00 9.82 + 0.00

∆Gethyl acetate kJ/mol) 5.55 + 0.09 6.22 + 0.05 7.26 + 0.00 8.03 + 0.00

∆Gacetone kJ/mol) 3.63 + 0.12 4.75 + 0.09 5.89 + 0.01 6.63 + 0.00

∆Gdichloromethane kJ/mol) 4.86 + 0.12 5.98 + 0.09 7.43 + 0.00 8.14 + 0.00

KA 0.0673 + 0.00 0.0753 + 0.00 0.0856 + 0.00 0.0955 +0.00

KB 0.0385 + 0.00 0.0685 + 0.00 0.120 + 0.00 0.128 + 0.00

KB/KA 0.572 + 0.02 0.910 + 0.00 1.402 + 0.00 1.337 + 0.00

γsD (mJ/m2) 34.03 + 0.66 34.15 + 0.12 35.27 + 0.02 33.49 + 0.04

93

The increase in basic and acidic character of the sucrose due to surfactant coating was in

good agreement with the higher spadsG∆ for four polar probes when compared to sp

adsG∆ of

pure sucrose crystals. The reasons behind the increase in basic character of the sucrose

surface due to surfactant can be explained only on the composition of Hodag CB6 used in

the present study. Since scarce information was readily available about the surfactant

Hodag CB6, the FTIR spectrum of Hodag CB6 was recorded and compared with some of

the well known food grade surfactants used in several industries.

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 2 4 6 8 10 12

DN/AN*

∆∆ ∆∆G

/AN

*

Pure sucrose

Surfactant coated

Fig. 6.5a. Plot of ∆∆∆∆G/AN* versus DN/AN* for sorption of polar probes onto pure

and surfactant coated sucrose at 313.05 K

94

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 2 4 6 8 10 12

DN/AN*

∆∆ ∆∆G

/AN

*

Pure scurose

Surfactant coated

Fig. 6.5b. Plot of ∆∆∆∆G/AN* versus DN/AN* for sorption of polar probes onto pure

and surfactant coated sucrose at 323.05 K

Fig. 6.6 shows the FTIR spectrum of Hodag CB6. This spectrum is in good resemblance

with the FTIR spectrum for soy-lecithin (Whittinghill et al., 2000) and polyester polyols

(polyricinoleate triols) (Petrovic et al., 2008). The peak at 3391 cm-1 represents the OH

stretching bond of water. The presence of phospholipids was confirmed by three

characteristic peaks which are at 2930 cm-1 due to CH2 stretching, between 1765 to 1720

cm-1 due to C=O vibration, between 1200 to 970 cm-1 due to both P-O-C and PO2

vibrations. The significant increase in basic character may be due to phospholipids such

as phosphatidyl-ethanolamine. The slight increase in acidic character due to the addition

of surfactant may be due to phospholipids such as phosphotidic acid.

95

Fig. 6.6. FTIR Spectrum of Hodag CB6.

The strength of solid/vapor interaction on the surface can be studied from the heat of

adsorption experiments. The heat of adsorption and the isosteric heat of adsorption are

related to the retention volume, VN, from the IGC experiments by (Kamdem et al., 1993)

[ ]( )Td

VdRqH N

d 1

ln==∆− (6.11)

RTqq dst += (6.12)

qd is the heat of adsorption, qst is the isosteric heat of adsorption. Eq. (6.11) assumes that

H∆ is independent of temperature. The isosteric heat of adsorption qst corresponds to the

heat developed when 1 mole of probe is adsorbed by an infinite amount of solid without

any change of fraction of the surface covered by the probe (Kamdem et al., 1993). The

96

H∆− values were calculated from the adsorption experiments using polar and neutral

probes at 313.05 and 323.05 K. Table 6.3 shows the calculated H∆− and the isosteric

heat of sorption for different probes. The sorption of basic, acidic and amphoteric probes

onto pure and surfactant coated sucrose was found to be endothermic and in the case of

neutral probes was found to be exothermic. This shows the difference in interactions

between polar and neutral probes with pure sucrose particles. For pure and surfactant

coated sucrose crystals, the qst for probes with higher DN/AN* (ethyl acetate) was found

to be higher when compared to probes with lower DN/AN* (acetonitrile). A similar effect

was reported in literature for the sorption of benzene compounds onto birch wood meal

(Kamdem et al., 1993). The higher qst for the probe with high DN number (ethyl acetate)

in the case of pure and surfactant coated sucrose crystals suggests a basic surface. The

greater increase in qst for ethylacetate in the case of surfactant coated crystals, suggest the

added surfactant significantly increased the basicity of the sucrose surface (Kamdem et

al., 1993). Likewise a slight increase in qst for acidic probe, dichloromethane, in the case

of surfactant coated crystals suggests a slight increase in acidity of the sucrose surface

(Kamdem et al., 1993).

97

Table 6.3. Enthalpy and isosteric heat of adsorption for the sorption of polar probes onto pure and surfactant coated sucrose

particles at 313.05 and 323.05 K.

-∆∆∆∆H, kJ/mol Pure sucrose Surfactant coated sucrose

Adsorbate Pure Surfactant qst(313.05K), kJ/mol qst(323.05 K), kJ/mol qst (313K.05), kJ/mol qst (323.05 K), kJ/mol

Heptane 11.29 + 5.08 29.37 + 0.30 13.89 + 5.08 13.98 + 5.08 31.98 + 0.30 32.06 + 0.30

Octane 9.32 + 0.34 34.19 + 0.26 11.92 + 0.34 12.01 + .34 36.79 + 0.26 36.87 + 0.26

Nonane 9.34 + 2.97 38.84 + 0.28 11.94 + 2.97 12.02 + 2.97 41.45 + 0.28 41.53 + 0.28

Decane 15.61 + 1.43 42.97 + 0.40 18.22 + 1.43 18.30 + 1.43 45.57 + 0.40 45.65 + 0.40

Undecane 16.71 + 0.18 47.86 + 0.36 19.31 + 0.18 19.40 + 0.18 50.46 + 0.36 50.54 + 0.36

Acetonitrile -35.31 + 7.22 -1.51 + 0.30 -32.71 + 7.22 -32.62 + 7.22 1.09 + 0.30 1.17 + 0.30

Ethyl acetate -15.76 + 3.30 -1.23 + 0.24 -13.16 + 3.30 -13.08 + 3.30 1.37 + 0.24 1.45 + 0.24

Acetone -36.08 + 7.37 -2.56 + 0.52 -33.48 + 7.37 -33.40 + 7.37 0.04 + 0.52 0.13 + 0.52

Dichloromethane -35.38 + 7.23 -2.26 + 0.45 -32.78 + 7.27 -32.70 + 7.27 0.35 + 0.45 0.43 + 0.45

98

From the adsorption science, during the growth of sucrose crystals in solution, the added

surfactants will get adsorbed onto the kink sites thereby reducing the surface energy of

the sucrose particles. The surface energy of the sucrose surface can affect the strength of

the particle-particle interaction. The adsorption of impurities (any substance other than

the material being crystallized) may either increase or decrease the growth rate of sucrose

crystals (Davey, 1976). The increase in growth rate due to decrease in interfacial tension

is usually referred to as thermodynamic effect of the added surfactant (Davey, 1976). The

inhibiting effect of impurity on the growth rate is due to the adsorption of impurities on

the kinks or terrace thereby reducing the step growth velocity.

Fig. 6.7. Plot of linear growth rate versus supersaturation ratio for different impurity concentrations at 30 oC. Fig. 6.7 shows the plot of linear growth rate versus supersaturation for the growth of

sucrose crystals in pure and impure solutions at 30 oC. From Fig. 6.7, it can be observed

that the growth rate of sucrose crystals increases with surfactant concentration at the

99

studied experimental conditions. In the present case, the increase in growth rate of

sucrose crystals due to decrease in surface energy was analyzed using ICG technique.

The surface energy of sucrose crystals grown under similar experimental conditions but

in the presence of surfactant was estimated using IGC. Fig. 6.8 shows the plot of

NVRT ln versus ( ) 5.0DLaN γ , for a homologous series of hydrocarbons and polar probes, of

sucrose particles grown in the presence of different surfactant concentrations at 313.05 K.

Fig. 6.8. NVRT ln versus ( ) 5.0DLaN γ plot for the adsorption of n-alkanes and polar

probes onto sucrose grown in the presence of impurities at 313.05 K.

From Fig. 6.8, it can be observed that the n-alkane line for sucrose crystals grown in the

presence of 0.0635 g/L of water lies above the n-alkane line for sucrose crystals grown in

100

the presence of 0.1271 g/L of water. A similar effect was observed at 323.05 K (not

shown here).

The surface energy of sucrose crystals decreases with increase in surfactant

concentration. This is in good agreement with Davey’s thermodynamic concept during

the growth of sucrose crystals. The calculated Dsγ for the sucrose crystals grown in the

presence of surfactant is given in Table 6.4. The effect of added surfactant on the specific

contribution to the free energy of adsorption spadsG∆ was determined using four polar

probes and is given in the same table. From Table 6.4, it can be observed that the added

surfactant alters the dispersive surface free energy and the surface polarity of the growing

sucrose crystals. This is due to the increase in both basicity and acidity of the sucrose

crystals due to the adsorption of surfactant onto the crystal surface (Table 6.2). The

increase in spadsG∆ and decrease in Dsγ with increasing

surfactant concentration suggest that the added surfactant increases the sites for specific

interaction and decreases the dispersive free energy due to the adsorption of surfactant

onto kink sites, respectively. So, the present study shows that IGC could be useful to

confirm the thermodynamic effect of an added impurity on the growth kinetics of crystals

in solutions.

Table 6.4. γγγγsD and sp

adsG∆ for polar and n-alkanes onto sucrose crystals grown in the presence of different surfactant concentration.

Surfactant

concentration: 0.0635 g/L of water

Surfactant

concentration: 0.1271 g/L of water

Parameter 313.05 K 323.05 K 313.05 K 323.05 K

∆Gacetonitrile (KJ/mol) 6.17 + 0.08 7.72 + 0.09 9.51 + 0.03 10.54 + 0.01

∆Gethyl acetate (KJ/mol) 5.66 + 0.04 6.68 + 0.08 5.21 + 0.02 6.86 + 0.01

∆Gacetone (KJ/mol) 3.63 + 0.11 5.41 + 0.08 4.99 + 0.05 6.98 + 0.01

∆Gdichloromethane (KJ/mol) 4.93 + 0.10 6.69 + 0.00 6.99 + 0.01 8.61 + 0.01

γsD (mJ/m2) 34.57 + 0.11 35.37 + 0.73 32.30 + 0.48 32.42 + 0.10

101

6.4. Conclusions

The well established IGC technique was found to be useful in determining the change in

surface free energy due to the adsorption of surfactant onto the surface of the sucrose

crystals. The surfactant increases the sites for specific interaction and decreases the

dispersive free energy due to the adsorption of surfactants onto kink sites respectively.

Coating sucrose with surfactants greatly alters enthalpy of adsorption and dispersive

surface free energy. The added surfactant also increases the surface acidity and basicity

of the sucrose surface. The increase in basic and acidic characteristics of the sucrose

surface were related to phospholipids such as phosphatidyl-ethanolamine and

phosphotidic acid. The IGC technique was found to be a useful technique to study the

thermodynamic effect of added impurities during the growth of crystals in solutions.

102

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Flour, S. and Papirer, E.J. (1983). Gas-solid chromatography: a quick method of

estimating surface free energy variations induced by the treatment of short glass

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Kinetic, thermodynamic and agglomeration effect of Kinetic, thermodynamic and agglomeration effect of Kinetic, thermodynamic and agglomeration effect of Kinetic, thermodynamic and agglomeration effect of

impurity in a crystal growth process using image analysisimpurity in a crystal growth process using image analysisimpurity in a crystal growth process using image analysisimpurity in a crystal growth process using image analysis

Abstract

The aim of the present investigation is to study the kinetic and thermodynamic effects of

Hodag CB6 (a non-ionic surfactant) on the growth rate of (110), (001), (100) faces of

sucrose crystals at 40 ºC using an offline image analysis technique. The growth process

was influenced by both the kinetic growth inhibition effect and the thermodynamic growth

promoting effect, the latter being predominant. The growth promoting effect of impurity

according to a multiple nucleation model was associated with the change in kinetic and

thermodynamic parameters. The coverage of impurity molecules onto different faces of

sucrose crystals follows a Langmuir isotherm at 40 ºC. The differential heat of

adsorption of the impurity onto sucrose surface, Qdiff, was found to be around 20 kJ/mol.

The activation energy for the growth process in pure and impure solutions was found to

be 67-68 and 68-69 kJ/mol, respectively.

7.1. Introduction

Impurities in supersaturated solutions significantly affect the growth, nucleation,

morphology, and also the agglomeration rate of the crystals. Impurities either increase or

decrease the growth rate of crystals depending on the surface properties of the crystal,

impurity and also on the solute. Some impurities may exhibit selective influence on a

particular crystallographic face. The impurities added to solution with the aim to either

alter the growth rate or to modify the crystallographic structure are in general called as

additives. The effects of additives can be classified as thermodynamic effects or kinetic

effects (Davey, 1976; Al-Jibbouri et al., 2002). Many investigations have been carried out

to explain the effect of impurities or additives on the growth kinetics. The inhibiting

effects of these on the growth of crystals are usually explained based on the mechanism

of impurity sorption in kinks and in terrace considering the kinetic effects (Al-Jibbouri et

106

al., 2002). On the other hand, the increase in growth rate is usually explained considering

the thermodynamic effect which is due to the adsorption of impurity on growing surface

leading to decrease in the surface energy (Davey, 1976; Kuznetsov et al., 2002; Sangwal

and Brzoska, 2001a; Sangwal and Brzoska, 2001b). Few studies are reported about the

thermodynamic effect of the added impurities on the crystal growth process (Davey,

1976; Kuznetsov et al., 2002; Sangwal and Brzoska, 2001a; Sangwal and Brzoska,

2001b).

Several kinetic models are used to explain the kinetic and thermodynamic effects

of impurities on crystal growth process. Kubota-Mullin (Kubota et al., 2000; Kubota,

2001) and Cabrera-Vermilyea (1958) models are the most widely used to explain the

inhibiting kinetics of the impurities on the crystal growth process. Recently the kinetic

effect of added impurity was proposed and explained based on a competitive sorption

model for the growth of sucrose crystals (Martins et al., 2006). BCF surface diffusion

model (Burton et al., 1951), multiple nucleation model (Sangwal, 1998) and a model

involving the complex source of cooperating dislocations (Sangwal, 2008) were found to

be excellent in explaining the kinetic and thermodynamic effects simultaneously.

In the present study the kinetic and thermodynamic effect of Hodag CB6 on the mean

growth rate of (110), (001), (100) faces of sucrose crystals were studied as a function of

supersaturation and impurity concentration at 40 oC. The mean face growth rates were

obtained using an offline image analysis technique. This technique already proved to be

one of the effective techniques in quantifying the variations of the crystal habit (Vucak et

al., 1998; Vucak et al., 1991; Bernard-Michel et al., 1999; Pons et al., 2005; Faria et al.,

2003; Ferreira et al., 2005). The morphology of particle population was explained using

different shape descriptors (Pons et al., 1998; Pons et al., 1997; Pons et al., 1999). Image

analysis techniques were widely used to explain the precipitation of calcium oxalate

(Bernard-Michel, 1999), morphology of sucrose crystals (Faria et al., 2003), calcium

carbonate precipitation (Vucak et al., 1998; Vucak et al., 1991), agglomeration of

gibbsite (Pons et al., 2005) and NaCl crystallization in presence of an impurity (Ferreira

et al., 2005).

The main objective of the present study is: (1) to check the applicability of the

theoretical kinetic models in predicting the kinetic and thermodynamic effect of

107

impurities on the individual face growth rate of sucrose crystals; and (2) to make use of

the well established image analysis technique to assist in predicting the kinetic and

thermodynamic effect of added impurity on the growing sucrose crystals in a batch

crystallizer and to study the effect of the added impurity on the final length of sucrose

crystals using the image analysis technique.

7.2. Materials and Methods

7.2.1. Experimental

Growth of sucrose crystals was made in a 4 L batch agitated crystallizer in isothermal

conditions at 40 oC (see Section 3.3). The agitation inside the crystallizer was maintained

at a constant speed of 250 RPM. Sucrose solutions were prepared by dissolving the

sucrose crystals at 60 oC in ultra pure water. Supersaturation was obtained by cooling

down the solution to working temperature (40 oC). All the experiments were carried out

for an initial supersaturation of 20 g of sucrose/100 g of water. Once the crystallizer

temperature was stable, accurately weighed amount of 16 g of sucrose seed crystals was

added into the crystallizer. Crystals ranging within the sieve fractions 355 to 425 µm

were used as seed crystals. The average seed size was determined using a laser size

analyzer (Coulter LS230) and was found to be 389 µm. In the present study, crystal

growth experiments were carried out in the presence of impurity (Hodag CB6) ranging

from 0.067 g/L of water to 0.268 g/L of water. The crystal growth experiments were

carried out for 24 hours until the supersaturation reaches roughly 7 g of sucrose/100 g of

water.

For image analysis, during each run, at regular time intervals, samples were

collected using a peristaltic pump and filtered through Schott Duran Buchner funnel with

perforated plate. The crystals were washed with ethyl alcohol and then spread over tissue

paper for drying. Care was taken to the possible extent to avoid breakage during the

drying process.

7.2.2. Image analysis

The microscopic pictures of the dried samples were obtained using a transmitted light

microscopy (Leica DMLB) with a monochrome camera (Leica DC 100) connected to PC,

where 8-bit grey level images of 768 x 576 square pixels are captured. VisilogTM5

(Noesis, Les Ulis, France) was used to analyse the captured images. These images are

108

then treated, analyzed and several numerical descriptors are extracted for each crystal

using VisilogTM5 (Noesis, les Ulis, France).

Before performing the measurements, the image treatment consists of: reduction

of color depth from 256 grey levels to two colors, hole-filling, noise-elimination,

elimination of the objects that contact the board of the image and identification of

particles in the image silhouette (Faria et al., 2003; Ferreira et al., 2005; Pons et al., 1999;

Bernard-Michel et al., 2002). After that, several image descriptors are obtained from each

crystal silhouette surface S from which the equivalent diameter 2 ⁄ is

deduced, perimeter P, number of internal zones N, Feret diameters distribution, from

which the maximal (Fmax) and minimal (Fmax) are deduced. The graphical capabilities of

VisilogTM5 were used to perform these operations easily and automatically. From these

parameters a set of secondary parameters are calculated and used for classification of

sugar crystals according to their complexity (Fig. 7.1) (Faria et al., 2003; Ferreira et al.,

2005; Pons et al., 1999; Bernard-Michel et al., 2002).

Fig. 7.1. Classification of sucrose crystals according to its complexity.

simple crystals (type A)

simple crystals (type B)

simple agglomerated

medium agglomerated highly

agglomerated

109

7.3. Results and Discussions

7.3.1. Quantifying agglomeration

Agglomeration is an important phenomenon which occurs in most of the crystallization

process (Bernard-Michel et al., 1999). Image analysis technique was already proved to be

an effective method in quantifying the agglomeration effect during the growth of crystals

in pure and impure solutions. In this study, image analysis was used to understand the

effect of added impurity on the agglomeration of the final sucrose crystals and its

influence on the final size of the crystals. Fig 7.1 shows the images of sucrose crystals

according to its complexity obtained by a light microscope. For automatic classification

of the crystals into different classes identified, sampling of crystals is a very important

step in image analysis, as it plays an important role on the reliability of the database to

represent the particle population. According to the literature, samples with 80 crystals

were successfully found to be sufficient to statistically represent the population of

calcium oxalate (Bernard-Michel et al., 1999) and barium sulphate crystals (Bernard-

Michel et al., 2002). In the present study, samples with 150 to 180 crystals were found to

represent statistically the crystal population. This was confirmed by comparing the

statistical results of two different sets of experiments, at the same conditions, containing

170 crystals. The difference between the average crystal sizes from the two different set

of images was found to 0.0188 mm. The details of number of crystals analyzed from each

experiment and the experimental conditions are given in Table 7.1.

To quantify the effect of impurity on the agglomeration degree of the final crystals, the

influence factor analysis was defined based on the made crystal classifications. The

influence factor analysis was proposed and used to describe the effect of shape of

precipitated barium sulphate on the size distribution (Bernard-Michel et al., 2002) and

also used to explain the agglomeration phenomena during the precipitation of calcium

oxalate ((Bernard-Michel et al., 1999). If Lmon and Lagg represent the average length of

monocrystals and agglomerated crystals, then the average length of the crystal population

can be defined by

( ) aggaggaggmon XLXLL +−= 1 (7.1)

where Xagg represents the fraction of agglomerated crystals. The length of crystals can be

obtained from the maximal Feret diameter using image analysis.

110

Defining the influence factor, INF, as (Bernard-Michel et al., 1999)

−= 1

mon

aggagg L

LXINF (7.2)

the relation between INF and the average length of sucrose crystals can be obtained from

Eqs. (7.1) and (7.2)

( )INFLL mon += 1 (7.3)

In the present research, the visual observation of the microscopic images showed

that agglomerated crystals can be classified into at least three types, simple agglomerated,

medium agglomerated and highly agglomerated crystals (Fig. 7.1). If Ls, Lm and Ll

represent the average length of simple, medium and highly agglomerated crystals,

respectively, the average length of agglomerated crystals can be defined by

Table 7.1. Experimental conditions and number of crystals analyzed to study the agglomeration effect of Hodag CB6 on the final crystals.

Experiment nº

ci, g/L of water

initial supersat uration (g of sucrose/100 g of

water)

final supersaturation (g of sucrose/100 g of

water) number of crystals

analyzed 1 0 20.0 4.7 182 2 0.067 20.0 6.5 181 3 0.268 20.0 3.6 142 2R 0.067 20.0 6.5 170R

R repeated with another set of images

[ ]llmmssaggagg XLXLXLXL ++= (7.4)

From Eqs. (7.3) and (7.4), the mean size of crystal population is given by

( )

−−+++= monl

mon

lm

mon

ms

mon

smon XX

L

LX

L

LX

L

LLL 11 (7.5)

In the present research, the effect of impurity on the INF was studied for different

impurity concentrations ranging from 0.067 to 0.268 g/L of water. Fig 7.2a shows the

plot of INF versus impurity concentration for the growth of sucrose crystals.

111

Fig. 7.2a. Effect of impurity concentration on the influence factor for the growth of sucrose crystals at 40 ºC.

From Fig 7.2a it can be observed that the INF values are equal to 0.12, approximately, for

the range of impurity concentrations studied. Eq. (7.3) shows that, if INF is equal or near

to zero, the agglomeration effect on crystal length can be neglected. According to the

results, the influence of the added impurity on the length of agglomerates is small, as

similar results were obtained for pure and impure systems. Fig 7.2b presents the plot of

the length of monocrystals, agglomerated crystals and the mean crystal length versus

impurity concentration, showing the influence of agglomeration on the size of final

crystals. This influence, as seen before, is small.

0.11

0.112

0.114

0.116

0.118

0.12

0 0.067 0.268

ci, g/L of water

INF

112

Fig. 7.2b. Effect of impurity concentration on the length of simple and agglomerated sucrose crystals (final crystal size) by image analysis.

7.3.2. Face growth kinetics and thermodynamics

To study the face growth kinetics of growing sucrose crystals, only monocrystals of type

A (Fig. 7.1) were considered. To calculate the individual face growth rate from the image

analysis, it is important to know the initial crystal dimensions. The basic linear

dimensions of sucrose crystals can be defined by the characteristic length of the crystal in

the crystallographic axis a, b and c as shown in Fig 7.3 (Bubnik and Kadlec, 1992). A

reliable measurement of sucrose crystals can be taken when the sucrose crystal lie on the

biggest face a (100 or 001 ) as shown in Fig 7.3. Fig 7.3 shows a monocrystals of type A

inscribed in a rectangle with three dimensions La, Lb and Lc. In this study, the average of

Fmax and Fmin of 60-80 monocrystals were used to understand the influence of added

impurity on the individual face growth kinetics of sucrose crystal. The Lb and Lc can be

determined easily from the Fmax and Fmin using image analysis. However it is very

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.067 0.268

ci, g/L of water

Leng

th o

f cry

stal

s, m

m

Monocrystals

Agglomerated

Lmean

113

difficult to measure the third dimension La. The average dimensions for a standard (flat)

sucrose crystal grown in laboratory is Lb:Lc:La = 1.60:1.0:0.73 (Bubnik and Kadlec,

1992). Belhamri and Mathlouthi (2004) determined the ratio of Lb/Lc for beet sugar

crystals as 1.33. In the present study, the images of the crystals grown in pure sucrose

solutions were used to determine the Lb/Lc ratio (or Fmax/Fmin). The ratio of Fmax/Fmin

obtained from the average of 1544 crystals using image analysis technique was found to

be 1.54, which is in good agreement with the reported values by Bubnik and Kadlec

(1992) (ranging from 1.54 to 1.68). Thus, in this study the third dimension, La was

calculated using the La/Lc = 0.73, reported by Bubnik and Kadlec (1992) and was also

assumed that this relation is not affected by the impurity, as the influence of the impurity

on the crystal size is not very significant..

The relation between the three basic linear dimensions of sucrose crystals

obtained by image analysis was used to study the effect of added impurities on the face

growth rate kinetics of sucrose crystals. This effect was determined using the crystal

samples collected from impure solutions at several time intervals during the growth

process. The ratio of Fmax/Fmin obtained from the average of 1280 monocrystals grown in

the presence of impurity using image analysis technique was found to be 1.51, which is

near to the value determined for the crystals grown in pure solution (1.54). This shows

that the added impurity does not have any elongation effect on the growing crystals for

the range of impurity concentrations studied. The Fmax, Fmin and Fmax/Fmin values obtained

were also used to calculate the growth rate of the different faces. According to Fig 7.4,

the determined face growth rates follow a power law growth kinetics as given by Eq.

(7.6)

nKR σ= (7.6)

where σ is the relative supersaturation, and R is the linear growth rate determined by

( )1

1

−−−

= −

nn

tt

tt

LLR nn (7.7)

where nt

L and 1−nt

L represent the length of growing face at time nt and 1−nt , respectively.

114

Lb

Lc

c-

c+

B- B+

Lb

Lc

La

The growth kinetic constant, K, and the reaction order, n, for the three growing faces

were determined by minimizing the error distribution between the R determined from

image analysis and obtained by Eq. (7.6). Error minimization was done by maximizing

the coefficient of determination defined by

( )( ) ( )( )2

_

2

__

2

__2

analysisimagen

analysisimageanalysisimage

analysisimageanalysisimage

RKRRR

RRr

−=−−

−=

σ (7.8)

The predicted kinetics according to Eq. (7.6) is shown in Figs. 7.4a to 7.4c. Figs. 7.4a to

7.4c show that the growth rate of sucrose crystals increases with increase in surfactant

concentration at the studied experimental conditions. The determined kinetic constants

and the corresponding r2 values are given in Table 7.2. The increase in growth rate could

be due to the decrease in surface free energy due to the adsorption of impurities at the

kink sites.

Fig. 7.3. Three characteristic lengths of sucrose monocrystal lying on (100) or (001 )

crystallographic face.

115

Fig. 7.4a. Experimental and power law kinetics for the growth of (110) face of sucrose crystal.

Table 7.2. Kinetic constant and order of reaction of power law expression for the

growing faces (110, 001, 100) of sucrose crystals.

(110) (001) (100)

ci, g/L of

water K, m/s n r2 K, m/s n r2 K, m/s n r2

0 5.80E-06 2.20 0.9945 2.37E-05 2.90 0.9918 1.73E-05 2.90 0.9918

0.067 1.80E-06 1.70 0.9753 2.50E-06 1.98 0.9681 1.80E-06 1.98 0.9681

0.268 2.00E-06 1.65 0.9679 3.80E-06 2.06 0.9684 2.80E-06 2.06 0.9684

0

0,000005

0,00001

0,000015

0,00002

0,000025

0,00003

0,000035

0 0,02 0,04 0,06 0,08 0,1

R, m

m/s

σσσσ

pure



116

0

0,000005

0,00001

0,000015

0,00002

0,000025

0 0,02 0,04 0,06 0,08 0,1

R, m

m/s

σσσσ

pure



Fig. 7.4b. Experimental and power law kinetics for the growth of (001) face of sucrose crystal.

117

Fig. 7.4c. Experimental and power law kinetics for the growth of (100) face of sucrose crystal. 7.3.2.1. Multiple nucleation model

The growth promoting and inhibiting effect of the added surfactant on the transient

kinetic behavior of the sucrose crystal faces was studied using a multiple nucleation

model given by (Sangwal, 2008; Mullin, 1993):

−=σ

σ FAR o exp6/5 (7.9)

where, the constants Ao and F in B-S model are given by Eqs. (7.10) and (7.11),

respectively:

( ) 3/12soo anhhcA Ω= β (7.10)

*.3

2

GXkT

hF ∆=

Ω= γπ (7.11)

0

0,000002

0,000004

0,000006

0,000008

0,00001

0,000012

0,000014

0,000016

0 0,02 0,04 0,06 0,08 0,1

R, m

m/s

σσσσ

pure



118

where, h is the height of elementary steps (m), co is the solubility of sucrose at

temperature T (K) (at 40 oC, co = 4.109 x 1027 molecules/m3 of water), Ω is the specific

molecular volume (m3), a is the dimension of growth units normal to the step (m) (in this

study, it is assumed a = h), γ is the surface free energy (J/m2) and *G∆ is the free

energy change required for the formation of stable two-dimensional nuclei on a perfect

surface.


( )σσF

AR

o −=

lnln

6/5 (7.12)

Thus the constants F and Ao for the different growing faces can be predicted from the

slope and intercept of the linear plot of

6/5

lnσ

R versus

σ1

. Figs. 7.5a to 7.5c show the

plot of

6/5

lnσ

R versus

σ1

at 40 oC for the growth of (110), (001) and (100) faces for the

range of impurity concentrations studied.

The effect of impurity concentration, ci, on the calculated thermodynamic and

kinetic parameter, F and Ao, are given in Table 7.3. Table 7.3 shows that both Ao and F

values decreases with increase in impurity concentration (in the case of (110) face, A0

decreases and then increases). According to the crystal growth theory, the increase in

growth rate, observed in Figs. 7.4, could be due to the decrease in surface free energy due

to the adsorption of impurities at the kink sites as reflected in the decrease in F value with

increasing impurity concentration. On the other hand, the decrease in Ao values suggests

that the reduction in velocity of steps is due to the sorption of impurities onto the kink

sites. As the growth rate increases with the impurity concentration in present work, the

thermodynamic effect was found to be dominating more than the kinetic effect of Hodag

CB6 on the sucrose crystals at the studied conditions. As mentioned before, the decrease

in F with increase in additive concentration could be explained based on the concept of

surface free energy which will be discussed in the following sections.

119

Table 7.3. Kinetic and thermodynamic parameters determined from multiple nucleation model. crystal face crystal face

110 001 100 110 001 100

ci, g/L of water F F F Ao, m/s Ao, m/s Ao, m/s

0 6.41E-02 9.73 E-02 9.73 E-02 3.86E-07 3.97E-07 2.90E-07

0.067 3.89 E-02 5.23 E-02 5.23 E-02 3.08E-07 2.48E-07 1.81E-07

0.268 2.44 E-02 3.71 E-02 3.71E-02 3.27E-07 2.41E-07 1.76E-07

Fig. 7.5a. Multiple nucleation kinetics for the growth of (110) face of sucrose crystals at 40 oC.

-10

-9,8

-9,6

-9,4

-9,2

-9

-8,8

-8,6

-8,4

-8,2

-8

0 10 20 30 40 50 60 70

ln(R

/ σσ σσ5/

6),)

mm

/s

1/σ1/σ1/σ1/σ

pure



120

Fig. 7.5b. Multiple nucleation kinetics for the growth of (001) face of sucrose crystals at 40 oC.

-11

-10,5

-10

-9,5

-9

-8,5

-8

0 10 20 30 40 50 60 70

ln(R

/ σσ σσ5/

6 ), m

m/s

1 /σ1 /σ1 /σ1 /σ

pure



121

Fig. 7.5c. Multiple nucleation kinetics for the growth of (100) face of sucrose crystals at 40 oC.

The determined F values from the kinetics, for the range of impurity concentrations, fit

the empirical expression given by

( )ivo cKFF −= 12/12/1 (7.13)

Likewise the relation between the kinetic parameter, Ao, for the studied crystal faces fits

the empirical expression given by

( )ioo zcAA −= 12/1*2/1 (7.14)

where oF and *oA are the values of F and oA when ic =0, respectively, and vK and z are

constants.

-11,5

-11

-10,5

-10

-9,5

-9

-8,5

-8

0 10 20 30 40 50 60 70

ln(R

/ σσ σσ5/

6 ),

mm

/s

1/σ

pure



122

The physical meaning of Eq. (7.13) can be explored by expressing it in terms of change

in free energy for the formation of stable nuclei.

Applying Eq. (7.11) in Eq. (7.13), the change in free energy for the formation of stable

nuclei in pure and impure solution as a function of impurity concentration can be

obtained

( )21** ivo cKGG −∆=∆ (7.15)

where *oG∆ denotes the vale of *G∆ when ci = 0.

When 1 >> Kvci, as in the present case, ( ) )1(1 2iviv cKcK −≈− , thus Eq. (7.15) can be

written as

( )ivo cKGG −∆=∆ 1** (7.16)

According to Eq. (7.16), the free energy change, *G∆ , decreases with increase in

impurity concentration ci.

Eq. (7.16) is in analogy with the classical nucleation theory, i.e., the overall free energy

required for the formation of critical nuclei under heterogeneous condition, must be less

than the corresponding free energy associated with homogeneous nucleation, i.e. (Mullin,

1993): hom** GG het ∆=∆ φ , where the factor φ is less than or equal to unity. The rate of

nucleation of solution can be affected considerably by the presence of impurities in the

system. The presence of impurity can induce the nucleation at degrees of super cooling

less than that required for spontaneous nucleation (Mullin, 1993). In the present case

from Eq. (7.16), the factor ( )ivcK−= 1φ obviously is less than or equal to unity and

decreases with the increase in impurity concentration. Thus, in the presence of impurities,

Eq. (7.13) can be used to study the effect of impurities on the thermodynamics by

considering the constant F of multiple nucleation model (Sangwal and Brzoska, 2001a).

The changes associated with the change in F and Ao value with increasing

impurity concentration could be explained by deducing the surface free energy and the

activation energy for the growth process from the experimental kinetics. Assuming

3/1Ω=h and using 3301004.715 m−×=Ω (Aquilano et al., 1983), the surface free energy

as a function of impurity concentration for sucrose crystals can be obtained from the

determined F values. The kinetic coefficient of steps, β, which is a function of impurity

concentration, ci, is determined from the constant Ao, assuming that the density of

123

adsorbed molecules, ns, is equal to the density of molecular positions, no, on the crystal

surface. The way to obtain no is discussed in later sections (refer to Eq. 7.29).

The activation energy for the step growth, W, can be calculated from β, using

( )kTWav /exp−=β (7.17)

where, v, is the frequency of atomic vibrations and is equal to 1013 s-1 (Burton et al.

1951).

The calculated kinetic coefficient, β, surface free energy,γ , and the activation energy for

the step growth, W, for the three studied faces at different impurity concentrations at 40 oC are given in Table 7.4. It must be noted that the activation energy obtained in this

study for pure system is in agreement with literature data, 65-70 kJ/mol (Bennema, 1968;

Shiau, 2003). From Table 7.4, it can be observed that the activation energy for the

growth, W, increases with impurity concentration and the opposite behavior was observed

with surface free energy. This indicates that the growth promoting effect, observed

previously, is associated to the thermodynamic effect. These effects can be analyzed as a

function of the coverage of impurity molecules onto the crystal surface. By rewriting Eq.

(7.13) in terms of interfacial tension, γ ,

( ) ( ) )1(2/12/1ii

o ckhkT

hkT

−Ω=Ωγγ

(7.18)

one obtains

)1( iio ck−= γγ (7.19)

Eq. (7.19) is similar to the Shishkovskii’s empirical isotherm (Sangwal, 2008):

( )]1ln1[ θγγ −−= Bo (7.20)

where θ is the surface coverage of the impurity and B is a constant and given by:

mo

kTB

ωγ= (7.21)

where mω is the surface area per adsorbed molecule and lies between 0.2-0.4 nm2

(Sangwal, 2008).

For low impurity concentrations, Langmuir isotherm transforms to a linear Henry type

expression and thus( ) iL cK==− θθ1ln . Eq. (7.20) can be written as:

]1[ iLo cBK−= γγ (7.22)

124

where, KL is the Langmuir constant given by (Sangwal, 2008):

=

RT

QK diff

L exp (7.23)

R is the gas constant and Qdiff is the differential heat of adsorption of the impurity on the

surface.

Thus the constant KL can be determined from the plot of oγγ / versus ci as shown in Fig.

7.6. Comparing Eqs. (7.19) and (7.22), the Langmuir constant, KL, is given by:

kT

kK moi

L

ωγ= (7.24)

In the present study, mω was assumed as 0.3 nm2. The determined KL values and the

differential heat of adsorption of the impurity on the surface, Qdiff, for the three growing

faces sucrose crystals are given in Table 7.5. The calculated Qdiff, was found to be around

20 kJ/mol for the sorption of surfactant molecules onto the three studied faces. Previously

Sangwal and Mielniczek-Brzoska reported the Qdiff, value in the range of 22 to 23 kJ/mol

and 8-155 kJ/mol for the sorption of Fe(III) ions (Sangwal and Brzoska, 2001a) and

Cr(III) ions (Sangwal and Brzoska, 2001b) onto different faces of ammonium oxalate

monohydrate single crystals.

125

Table 7.4. Kinetic constant, surface free energy and energy of activation for the growth of crystals for pure and impure system by multiple nucleation model during the growth of (110), (001), and (100) faces of sucrose crystals.

Impurity concentration(g/L

of water)

Kinetic constant, ββββ, m/s Surface free energy, γγγγ, J/m 2 Activation energy for growth, W, KJ/mol

(110) (001) (100) (110) (001) (100) (110) (001) (100) 0 5.21E-08 5.36E-08 3.92E-08 1.34E-03 1.65E-03 1.65E-03 67.4 67.3 68.1

0.067 4.16E-08 3.35E-08 2.44E-08 1.04E-03 1.21E-03 1.21E-03 67.9 68.5 69.3 0.268 4,42E-08 3.26E-08 2.38E-08 8.25E-04 1.02E-03 1.02E-03 67.8 68.6 69.4

126

Fig. 7.6. Shishkovskii isotherm for the sorption of Hodag CB6 onto sucrose surface

at 40 oC.

The calculated KL values can be used to determine the coverage of surfactant

molecules onto the crystal surface, θ , using the Langmuir expression. According to a

Langmuir isotherm, a linear relation was observed between the solute coverage and

impurity concentration for the conditions studied (not shown). Experiments were not

performed with impurity concentrations above 0.268 g/L of water as the present

investigation is to study the effect of impurity concentration (Hodag CB6) at the level

used in the sugar industries.

Table 7.5. Langmuir constant, KL, values and differential heat of adsorption of the impurity on the surface, Qdiff, for the three growing faces of sucrose crystals.

face KL,L/g KL x 10-3 (L/mol)

Qdiff (KJ/mol)

110 0.143 2.00 19.8 001 0.180 2.52 20.4 100 0.180 2.52 20.4

0,50

0,60

0,70

0,80

0,90

1,00

1,10

0 0,05 0,1 0,15 0,2 0,25 0,3

γ/γ

0

ci, g/L of water

(110) face

(001) and (100) faces

127

7.3.2.2. Burton-Cabrera-Frank model

The growth rate of sucrose crystals according to a BCF surface diffusion model is given

by (Burton et al., 1951)

( )σσ

σσσ/

/tanh

1

1cR = (7.25)

Eq. (7.25) can explain the growth process if the kinetics was controlled by surface

diffusion.

1σ is given by

skTλγσ Ω= 5.9

1 (7.26)

and the constant, c, by (Sangwal and Brzoska, 2001a):

ββ

ΩΛ=

a

nc o1 (7.27)

1β and Λ are dimensionless factors less than unity describing the influence of the steps

and the kinks in steps, respectively (Sangwal, 2008). no is the concentration of growth

units on the surface (particles/m2), Ω is the specific molecular volume of molecule or

atom (m3), a is the dimension of the growth unit normal to the advancing step (m), sλ is

the average diffusion distance of the growth units on the surface (m), assumed to be, in

this work, 10a (Sangwal and Brzoska, 2001a), k is the Boltzmann constant, and T is the

temperature, K.

Assuming, 11 ≈Λβ , according to Burton-Cabrera-Frank model one obtains:

∆−Ω=

kT

Gvnc ads

o exp (7.28)

where ∆Gads is the total adsorption energy which is the sum of adsorption energy factors:

from the solution to the surface and from the surface to the kink where the growth unit is

incorporated into the crystal surface. The parameter no refers to the number of molecular

positions available for adsorption on the crystal surface, given by (Koutsopoulus, 2001):

m

sucrosesucrose

m

toto A

mSSA

A

An == (7.29)

128

where Atot is the total surface area of the sucrose crystals available for growth in

supersaturated solution, SSAsucrose is the specific surface area of the sucrose crystals and

msucrose is the mass of seed crystals and Am is the area occupied by one molecule and is

equal to 3/2Ω . From the specific surface area of sucrose calculated from the BET analysis

(1 m2/g, approximately), no was determined as 2.00 x 1019 positions/m2. The Gibbs free

energy for adsorption of sucrose molecule from solution onto the crystal surface and

incorporation into a kink can be calculated by rearranging the Eq. (7.28)

vn

ckTG

oads Ω

−=∆ ln (7.30)

when σσ1 >>1 the growth law exhibits non-linear behavior given by:

2

1

σσc

R = (7.31)

Using the kTγ value from multiple nucleation model, the BCF expression can be

solved to analyze the kinetic effect of the added impurity on the growth kinetics. A non-

linear regression technique was used to solve Eq. (7.31). The non-linear regression

involves the maximization of coefficient of determination between the experimental data

and Eq. (7.31) using solver add-in, Microsoft Excel, Microsoft Corporation. Figs. 7.7a to

7.7c show the experimental data and predicted BCF surface diffusion kinetics by non-

linear regression for the growing faces (110), (001) and (100), respectively.

129

Fig. 7.7a. Experimental data and BCF kinetics for the growth of (110) face of


The r2 values between the experimental data and the predicted BCF kinetics for the

studied faces, for the range of impurity concentrations studied, were in the range of 0.78-

0.94. Though the kinetic fit was not excellent under few experimental conditions, the

determined kinetic constants were found to be helpful in studying the underlying

mechanism. Since the fit of multiple nucleation model was reasonable for the

experimental data obtained in

0

0,000005

0,00001

0,000015

0,00002

0,000025

0,00003

0,000035

0,00004

0 0,02 0,04 0,06 0,08 0,1

R, m

m//

s

σσσσ

pure



BCF

130

Fig. 7.7b. Experimental data and BCF kinetics for the growth of (001) face of


this study, the surface free energy determined from the multiple nucleation model was

used to determine the constant 1σ for the range of impurity concentrations studied. The

predicted c and the constant 1σ for the (110), (001) and (100) faces, as a function of the

impurity concentration at 40 oC are given in Table 7.6. The calculated c values were

found to differ from the values obtained by Bennema (1968) for the sucrose crystals at 40 oC by a magnitude of 10. Table 7.6 shows that the increase in growth rate with impurity

concentration was associated, globally, with the simultaneous decrease in the constants c

and 1σ . This was in good agreement with the results obtained from the multiple

nucleation model, so that growth promoting effect was associated with the decrease in

interfacial energy.

0

0,000005

0,00001

0,000015

0,00002

0,000025

0,00003

0,000035

0,00004

0 0,02 0,04 0,06 0,08 0,1

R, m

m/s

σσσσ

pure



BCF

131

Fig. 7.7c: Experimental data and BCF kinetics for the growth of (100) face of


The change in total adsorption energy ∆Gads with increase in impurity concentration,

according to BCF model, obtained using Eq. (7.30) is given in Table 7.6, and found to be

in the range of 66 to 69 kJ/mol, except for (001) face at the higher impurity

concentration.

Table 7.6. Kinetic and thermodynamic parameter in the BCF equation for the growth of (110), (001), (100) crystal faces of sucrose at 40 oC.

c, m/s ∆∆∆∆Gads (kJ/mol) σσσσ1 ci, g/L of water (110) (001) (100) (110) (001) (100) (110) (001) (100)

0 9.80E-07 7.81E-07 5.70E-07 66.9 67.5 68.3 0.235 0.290 0.290 0.067 6.50E-07 4.84E-07 3.54E-07 68.0 68.8 69.6 0.183 0.212 0.212 0.268 8.17E-07 5.78E-05 1.07E-06 67.4 56.3 66.7 0.145 0.179 0.179

0

0,000005

0,00001

0,000015

0,00002

0,000025

0,00003

0,000035

0,00004

0 0,02 0,04 0,06 0,08 0,1

R, m

m/s

σσσσ

pure



BCF

132

7.4. Conclusions

The widely accepted image analysis technique was successfully used to study the effect

of a non-ioninc surfactant on the growth rate different faces of sucrose crystals at 40 oC.

The length of agglomerated crystals and the length of monocrystals are found to be not so

different, quantified from the influence factor for the range of impurity concentration

studied. By image analysis, the growth rate of (110), (001) and (100) faces of sucrose

crystals were found to be increasing with surfactant concentration. The growth

promoting effect of non-ionic surfactant on the kinetics of sucrose crystals in solution

was explained using a multiple nucleation model and BCF diffusion model. Both the

models successfully represent the kinetics of sucrose crystal growth process for the range

of surfactant concentrations studied. The growth process was influenced by both the

kinetic growth inhibition effect and the thermodynamic effect, the latter being

predominant for the range of surfactant concentrations studied. The growth promoting

effect was due to decrease in the surface free energy induced by the addition of

surfactant. The decrease in the kinetic parameter was found associated with the increase

in activation energy for the growth of crystal faces. The coverage of impurity molecules

onto different faces of sucrose crystals follows a Langmuir isotherm at 40 oC.

133

7.5. References



Aquilano, D., Franchini-Angela, M. and Rubbo, M. (1983). Growth morphology of polar

crystals: A comparison between theory and experiment in sucrose. J. Cryst. Growth.

61, 369-376.

Belhamri, R. and Mathlouthi, M. (2004). Effect of impurities on sucrose crystal shape

and growth., Curr. Top. Cryst. Growth. Res. 7, 63-70.


Growth. 3, 331-334.

Bernard-Michel, B., Pons, M.N., Vivier, H. and Rohani, S. (1999). The study of calcium

oxalate precipitation using image analysis. Chem. Eng. J. 75, 93-103.

Bernard-Michel, B., Pons, M.N. and Vivier, H. (2002). Quantification, by image analysis,

of effect of operational conditions on size and shape of precipitated barium sulphate.

Chem. Eng. J. 87, 135–147.

Bubnik, Z. and Kadlec, P. (1992). Sucrose crystal shape factor., Zuckerind. 117, 345-350.


equilibrium structure of their surfaces. Philos T R Soc A. 1934, 299-358.

Cabrera, N., Vermilyea, D.A. in: R.H. Domeus, B.W. Roberts, D. Turnbull, (Eds.),

(1958). Growth and perfection of crystals, Wiley, New York.


from solution., J. Cryst. Growth. 34, 109-119.

Faria, N., Pons, M.N., Azevedo, S.F., Rocha, F.A. and Vivier, H. (2003). Quantification

of the morphology of sucrose crystals by image analysis., Powder Technol. 133, 54-

67.

Ferreira, A., Faria, N., Rocha, F., Azevedo, S.F.D. and Lopes, A. (2005). Using image

analysis to look into the effect of impurity concentration in NaCl crystallization.,

Trans. IChemE, Part A. 83(A4), 331-338.


Langmuir. 17, 8092-8097.

134


Technol. 36, 8-10.


supersaturation and impurity concentration on crystal growth., J. Cryst. Growth. 212,

480-488.


organic impurities on growth kinetics of KAP and KDP crystals., J. Cryst. Growth.

193, 164-173.

Martins, P.M., Rocha, F.A. and Rein, P. (2006). The influence of impurities on the crstal

growth kinetics according to a competitive adsorption model., Cryst. Growth Des.

6(12), 2814-2821.


Pons, M.N., Vivier, H. and Rolland, T. (1998). Pseudo-3D shape description for facetted

materials. Part. Part. Syst. Charact. 15, 100-107.

Pons, M.N., Vivier, H. and Dodds, J. (1997). Particle shape characterization using

morphological descriptors., Part. Part. Syst. Charact. 14, 272-277.

Pons, M.N., Vivier, H., Belaroui, K., Bernard-Michel, B., Cordier, F., Oulhana, D. and

Dodds, J.A. (1999). Particle morphology: from visualisation to measurement. Powder

Technol. 103, 44–57.

M.N. Pons, V. Plagnieux, H. Vivier, D. Audet, Comparison of methods for the

characterisation by image analysis of crystalline agglomerates: The case of gibbsite,

Powder Technol. 157 (2005) 57 – 66..

Sangwal, K. (1998).Growth kinetics and surface morphology of crystals grown from

solutions: Recent observations and their interpretations., lProg. Cryst. Growth

Charact. Mater. 36, 163-248


applications, John Wiley & Sons, Ltd, England.


ammonium oxalate monohydrate crystals from aqueous solutions. J. Cryst. Growth.

233, 343-354.

135

Sangwal, K. and Brzóska, M.E. (2001b). On the effect of Cu(II) impurity on the growth

kinetics of ammonium oxalate monohydrate crystals from aqueous solutions., Cryst.

Res. Technol. 36, 837-849.

Shiau, L.-D. (2003). The distribution of dislocation activities among crystals in sucrose

crystallization., Chem. Eng. Sci. 58, 5299-5304.

Vucak, M., Peric, J. and Pons, M.N. and Chanel, S. (1999). Morphological development

in calcium carbonate precipitation by the ethanolamine process., Powder Technol.

101, 1-6.

Vucak, M., Pons, M.N., Peric, J. and Vivier, H. (1998). Effect of precipitation conditions

on the morphology of calcium carbonate: Quantification of crystal shapes using

image analysis., Powder Technol. 97, 1-5


A simple model to explain the rate of change in A simple model to explain the rate of change in A simple model to explain the rate of change in A simple model to explain the rate of change in

dislocation dislocation dislocation dislocation activity oactivity oactivity oactivity of the crystalf the crystalf the crystalf the crystal surfaces of crystal surfaces of crystal surfaces of crystal surfaces of crystal

collective during a growth process in a batch collective during a growth process in a batch collective during a growth process in a batch collective during a growth process in a batch

crystallizercrystallizercrystallizercrystallizer

Abstract

Kinetic model is proposed from the concepts of Burton-Cabrera-Frank (BCF) theory

to explain the change in activity of dislocation spirals on the surfaces of crystal

collective during a crystal growth process in diffusion and in kinetic regime. The

model was proposed assuming that the change in activity of crystals decreases with

time (i.e., changing supersaturation) and follows a first order kinetics irrespective of

the growth process in diffusion or in kinetic regime. The proposed model was fitted to

explain the experimental growth kinetics of sucrose in solutions at different

temperatures and agitation speeds. The proposed model represents well the

experimental data for the range of experimental conditions studied. The proposed

model is very simple to use and for the first time incorporates the parameter to

explain the change in activity of dislocation spirals during a crystal growth process.

The proposed model has the advantage to estimate the kinetic constant of the growth

process and the rate of change in activity of dislocation spirals on the crystals surface

simultaneously. The total energy of adsorption for the growth of sucrose crystals was

determined using the proposed model and was found to be, approximately, 93 and 92

kJ/mol at 30 and 40 oC, respectively.

8.1. Introduction

Crystal growth often occurs at active sites where dislocations emerge from the crystal.

Burton-Cabrera-Frank theory explains the growth rate distribution of crystals based

on the dislocation activity on the surface of various nuclei resulting in different

growth rate (Burton et al., 1951). The dislocations on the crystal surfaces may be due

to edge or screw dislocations or can have any degree of mixed type dislocations for

generating the steps for crystal growth (Shiau, 2003). In a batch crystallization

process, it is obvious that the supersaturation changes with the growth of crystals

138

during the growth process which in turn will influence the activity of dislocations on

the crystal surface.

To make the evidence of the influence of dislocations on the crystal growth

process, two models have been proposed in literature reporting the effect of activity of

dislocations on the growth rate distribution of crystals. Randolph and White (1977)

proposed a random fluctuation model assuming that the growth rate of an individual

crystal fluctuates in the course of time. A constant crystal growth model of Berglund

(1980) claims that the individual crystal has an inherent growth rate that is constant,

but different crystals have different inherent growth rates. It is believed and accepted

by several researchers the GRD during the growth of crystals be due to the activity of

dislocations on the crystal surface (Burton et al., 1951; Shiau, 2003; Randolph and

White, 1977; Berglund, 1980; Berglund and Murphy, 1986; Garside et al., 1976;

Lacmann et al., 1999). However, to the best of the knowledge is concerned, no studies

have been reported explaining the rate of change in activity of dislocation spirals,

which is expected during a course of time in a batch crystal growth process. A closely

relevant work was made and reported recently by Shiau (2003) to explain the

distribution of dislocation activities among crystals for sucrose crystallization process

based on a modified two step crystal growth model. The objective of the present study

differs from the previous works (Shiau, 2003; Randolph and White, 1977; Berglund,

1980; Berglund and Murphy, 1986; Garside et al., 1976) and the approach is more

likely kinetics (Chemical Reaction Engineering approach) than mechanistic. The idea

behind this study was originally obtained from the deactivation kinetics for catalysts

which was put forward by Park and Levenspiel (Park and Levenspiel, 1976).

In this study, the deactivation kinetics of dislocation activity which is expected

due to the change in supersaturation that decreases with reaction time, irrespective of

the limiting step (diffusion or surface reaction) during a batch crystallization process,

was studied using the sucrose crystals growth experiments. A kinetic model was

proposed to explain the kinetics of change in dislocation activities on the crystal

surfaces for the limiting conditions of surface diffusion and surface integration. The

kinetics was proposed assuming that the kinetics of deactivation of dislocation

activities follows a first order process. The proposed kinetic model was used to

explain the rate of change in activities on the surface of sucrose crystals (collective)

during the growth process in pure solutions at different temperatures and agitation

speeds. The aim of the present work is not to model the growth rate dispersion;

139

instead it is limited to model the kinetics of the growth process considering the change

in activity of dislocation spirals on the collective crystal surfaces at the studied

experimental conditions.

8.2. Experimental

8.2.1. Sucrose

Sucrose crystals were obtained from RAR sugar refineries, Porto, Portugal. The

obtained sucrose was sieved through 425 to 500 screens and used as seed crystals

during the growth experiments. The average seed size was determined using a laser

size analyzer (Coulter LS230) and was found to be 5.36 x 10-4 m.

8.2.2. Crystal growth experiments

Growth of sucrose crystals was carried out at two different temperatures, 30 and 40 ºC

in the crystallizer shown in Fig. 3.1. The experiments were carried out, unless

specified, at a constant agitation speed of 250 RPM. The experiments were carried out

for 24 to 72 hours, depending on the solution temperature. The mass of the crystals

inside the crystallizer at any time was calculated from mass balance as explained in

Section 3. 3.

8.3. Results and discussions

The growth rate of sucrose crystals according to a BCF surface diffusion model is

given by

( )σσ

σσσ/

/tanh

1

11cR = (8.1)

The constants, c1 and 1σ are complex temperature dependent constants given by

ββ

ΩΛ=

a

nc o1

1 (8.2)

sskTλγσ Ω= 19

1 (8.3)

1β and Λ are dimensionless factors less than unity describing the influence of the

steps and the kinks in steps, respectively. no is the concentration of growth units on

the surface (particles/m2), Ω is the specific molecular volume of molecule or atom

(m3), a is the dimension of the growth unit normal to the advancing step (m), sλ is the

average diffusion distance of the growth units on the surface (m) that ranges from 10-

100a, k is the Boltzmann constant, T is the temperature, K, and s is a measure of

140

strength of the source of cooperating spirals. Bennema and Gilmer (1973) suggested

that s will be in the range of 1 to 10.

When, σσ /1 >>1, the growth law exhibits non-linear behaviour given by:

2

1

1 σσc

R = (8.4)

Eq. (8.4) holds true only for a process limited by a second order surface integration

kinetics. For a process limited by diffusion step, i.e., higher supersaturation, the BCF

expression reduces to

σ1cR = (8.5)

Eqs. (8.4) and (8.5) can be written in terms of overall growth rate expression given by

22σkRg = (8.6)

σ1kRg = (8.7)

where the constants k1 and k2 are related to surface reaction constant and to the shape

factors of crystal.

11

3c

f

fk

s

cv ρ= (8.8)

=

1

12

3

σρ c

f

fk

s

cv (8.9)

fv and fs are the volume and area shape factor of the sugar crystal.

From the concepts of BCF theory, the dislocation activity of a crystal corresponds to

the growth rate dispersion in crystals, thus considering the dislocation activities of

crystals, gR ,for a diffusion controlled and surface reaction controlled growth process

can be given by (Shiau, 2003)

σ1akRg = (8.10)

22σakRg = (8.11)

where a is the dislocation activity of growing crystals (crystal collectives), which was

assumed to decrease with run time according to a first order expression given by

akdt

dad=− (8.12)

kd is the deactivation (of dislocation activity) kinetic constant (s-1)

Integrating Eq. (8.12), the dislocation activity of growing crystals is given by

( )tkaa do −= exp (8.13)

141

For unit dislocation activity of crystals, ao will be equal to unity when time t = 0:

( )tka d−= exp (8.14)

If co and c represent the initial concentration and concentration of solute at any time, t,

the crystallized mass at any time, t, is given by

( ) so Vccm −= (8.15)

From Eqs. (8.10) to (8.15), the rate of crystal growth limited by a diffusion and

integration step, respectively, can be written as

( )( )sdsss

cv cctkccVf

Af

dt

dc −−=− exp3

1

ρ (8.16)

( )( )2

1

12

exp3

sdsss

cv cctkc

cVf

Af

dt

dc −−

=−

σρ

(8.17)

sV is the volume of solvent (water) and A is the area of crystals. sc is the solubility.

With respect to initial process conditions, the limiting conditions to solve Eq. (8.16)

and Eq. (8.17) are given by

c = co; t = 0 and

c = c; t = t (8.18)

Applying Eq. (8.18) in Eq. (8.16), for a process limited by diffusion, the growth

kinetics is given by

( )tk

dsss

cv

s

os dek

c

cVf

Af

cc

cc −−=

−−

13

ln 1ρ (8.19)

A was considered constant and equal to the average crystals area between t=0 and t=t.

This assumption is valid if the change in A is small.

According to Eq. (8.19), for the condition, t∞ , in the diffusion regime, the

concentration does not drop to saturation, instead is governed by the rate of reaction

or the dislocation activities of the crystal surfaces.

dsss

cv

s

os

k

c

cVf

Af

cc

cc 13ln

ρ∞

∞

=

−−

(8.20)

Combining Eqs. (8.19) and (8.20), the expression explaining the deactivation kinetics

of dislocation activities under diffusion regime during a crystal growth process, and

considering a small variation for A, is given by

tkcckVf

f

cc

cc

A dsdss

cv

s

s −

=

−−

− ∞1

3lnln

1ln

ρ (8.21)

142

Likewise for a growth process limited by surface integration, the kinetic expression

can be obtained by integrating Eq. (8.17) with respect to limiting conditions in Eq.

(8.18)

( )tk

dsss

cv

oss

dek

c

cVf

Af

cccc−−

−

−=

−1

311

1

12 σ

ρ (8.22)

According to Eq. (8.22), for the condition, t ∞ , the concentration does not drop to

saturation, instead is governed by the rate of reaction or deactivation of the dislocation

activities on the crystal surface

−

−=

−∞

∞ 1

12

311

σρ

dsss

cv

oss k

c

cVf

Af

cccc (8.23)

Combining Eqs. (8.22) and (8.23), the growth kinetic equation, considering small

variation for A, is given by

tk

dsss

cv

ss

dek

c

cVf

Af

cccc−

∞

=

−−

− 1

12

311

σρ

(8.24)

The simplified expression explaining the deactivation kinetics of dislocation activity

under kinetic regime during a crystal growth process is given by

( ) tkk

c

cVf

fy d

dsss

cv −

=

1

12

3lnln

σρ

(8.25)

where, y, in Eq. (8.25) is given by

Accccy

ss

111

−−

−=

∞

(8.26)

Eqs. (8.21) and (8.25) proposed in this study can be useful to model the kinetics of

crystal growth process and the associated change in dislocation activities of crystals in

the diffusion and in the kinetic regime respectively.

Fig. 8.1 shows the plot of concentration versus time during the growth of sucrose

crystals in pure solutions at three different agitation speeds, 150, 250 and 400 RPM,

respectively. Fig. 8.1 shows that the kinetic profile can be roughly divided into tow

regimes, the initial profile followed by an exponential curve. The initial linear portion

represents the rapid growth rate of sucrose crystals followed by a slower growth

phase. This effect can be explained by considering the decrease in supersaturation

during the crystal growth process. The decrease in supersaturation, by the concepts of

BCF theory, will decrease the activity of dislocations in the surface of crystals leading

to a decrease in growth rate as observed from the exponential profile of the growth

143

kinetics. The kinetic profile of growth of sucrose crystals following the deactivation

kinetic model as in Eq. (8.21) and (8.25) are shown in Figs. 8.2a and 8.2b,

respectively. The calculated kinetic constant, c1, and deactivation rate constant, kd,

values are given in Table 8.1.

2360

2380

2400

2420

2440

2460

2480

2500

2520

2540

2560

0 500 1000 1500 2000 2500

Time, min

c,g/

L

150 RPM

250 RPM

400 RPM

Fig. 8.1. Concentration profile during the growth of sucrose crystals at 313 K.

From Table 8.1, it can be observed that the experimental kinetic data was equally

represented by both a first order and second order growth kinetic expressions. Both

the kinetic expressions represent the growth kinetics with high r2 values, however the

calculated kinetic constant, c1, using Eq. (8.21) is physically unrealistic. Thus in the

present study, the process was assumed to follow a second order surface integration

kinetics. The kinetic rate constant, c1, and the rate constant corresponding to the

deactivation kinetics of dislocation activities of growth spirals, kd, are determined

from the intercept and slope of Fig. 8.2b using Eq. (8.25). 1σ was obtained by

assuming γ = 10-3 J/m2, s = 1 and λs = 10a. Table 8.1 shows that kd and c1 values

increases with agitation speed.

144

Table 8.1. Determined kinetic coefficient and the corresponding coefficient of determination by Eqs. (8.21) and (8.25) for the growth of sucrose crystals in pure solutions.

Surface diffusion kinetics, Eq. (8.21) Surface integration kinetics, Eq. (8.25) Agitation

speed, rev.min-1 Temperature, ºC kd, s

-1 c1,m/s r2 kd,s-1 c1, m/s

ββββ, m/s r2 ∆∆∆∆Gads, kJ/mol 150 40 2.16E-05 0.012 0.988 2E-05 2.75E-15 8.01E-14 0.980 92.9 250 40 2.5E-05 0.187 0.954 2.166E-05 4.02E-15 1.17E-13 0.941 91.9 400 40 3.0E-05 0.215 0.972 2.66E-05 4.89E-15 1.42E-13 0.963 91.4 250 30 -- -- -- 5E-06 2.72E-14 7.92E-14 0.964 92.8

145

Fig. 8.2a. Plot of

−−

− ∞

cc

cc

A s

sln1

ln versus time, t, for the growth of sucrose

crystals for different agitation speeds at 313 K.

-7

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

0 500 1000 1500 2000 2500

Time, min

Ln

(y)

150 RPM

250 RPM

400 RPM

Fig. 8.2b. Plot of lnAcccc ss

111

−−

− ∞

versus time, t, for the growth of sucrose

crystals for different agitation speeds at 313 K.

146

Several reasons can be attributed for the increase in kd and c1 with increase in

agitation speed. Increase in agitation may increase the turbulence around crystals with

the solution in immediate contact enhancing the surface roughness which is related

with the activity of dislocation spirals. The impingement of crystal molecules on the

crystal surface may cause an increase in energy of crystal collisions, which in turn

will increase the amount and severity of damage to the crystal surface (Garside et al.,

1976) at higher agitation speeds. There is no general evidence explaining the

influence of the activity of dislocation density on the diffusion or the surface

integration step during a crystal growth process. Based on the kinetic expression it is

possible get one idea about the influence of dislocation activities on the crystal growth

process and its variation with time during a growth process.

The decrease in activity of dislocation spirals on the surface with time can be

explained from the concepts of roughness. Pantaraks et al. (2005) show that the

growth rate of potash alum at high supersaturations causes significant roughening of

the surface, presumedly due to the differences in perfection of lattice integration. The

same authors reported that the effect of surface roughness can be healed by extended

periods of crystal growth at low levels of supersaturation, which is the case in this

study during the growth of sucrose crystals. More recently Ferreira et al. (2008)

explained this effect for the case of growing sucrose crystals at different

supersaturations.

The integration limited growth of sucrose crystals following dislocation

deactivation kinetics according to the proposed model, Eq. (8.12), in this study at 303

and 313 K is shown in Fig. 8.3. The experimental data was well represented by the

proposed model. The good fit of experimental data show the successfulness of the

model in representing the experimental growth kinetics of sucrose crystals at the

studied conditions.

147

-6

-5

-4

-3

-2

-1

0

0 500 1000 1500 2000 2500

Time, min

Ln

(y)

303 K

313 K

Fig. 8.3. Plot of lnAcccc ss

111

−−

− ∞

versus time, t, for the growth of sucrose

crystals at 303 and 313 K.

Assuming 1β and Λ in Eq. (8.2) equal to unity, the kinetic constant β can be

obtained from the determined constant c1 (Sangwal and Brzóska, 2001).

Ω=

on

ac1β (8.27)

The kinetic constant, β, is related to ∆Gads, which is the total adsorption energy which

is the sum of adsorption energy factors: from the solution to the surface and from the

surface to the kink where the growth unit is incorporated into the crystal surface by

the relation

∆−=

kT

Gav adsexpβ (8.28)

The parameter no refers to the number of molecular positions available for adsorption

on the crystal surface, given by

m

sucrosesucrose

m

toto A

mSSA

A

An == (8.29)

where Atot is the total surface area of the sucrose crystals available for the growth of

crystals in supersaturated solution, SSAsucrose is the specific surface area of the sucrose

148

crystals, msucrose is the mass of seed crystals and Am is the area occupied by one

molecule and is equal to 3/2Ω . From the specific surface area of sucrose calculated

from the BET analysis, no was determined as 2.00 x 1019 positions/m2. Assuming

phkTv /= (hp refers to Planck’s constant), the Gibbs free energy for adsorption of

sucrose molecule from solution onto the crystal surface and incorporation into a kink

can be calculated by rearranging the Eq. (8.28).

Table 8.1 shows the calculated ∆Gads values at the studied conditions. From

Table 8.1, it can bee observed that the total energy of adsorption for the growth of

sucrose crystals at 303 and 313 K was found to be, approximately, 93 and 92 kJ/mol,

respectively. For most of the crystal growth processes limited by diffusion and

integration step, the activation energy would be in the range of 10 – 20 kJ/mol and 40

– 60 kJ/mol respectively (Sangwal and Brzóska, 2001). In this study, the determined

values are more near the values of activation energy reported by Bennema (1968)

(65.7-69.9 kJ/mol) and by Ouizzane et al. (2008) (78.75 kJ/mol) for the growth of

sucrose crystals in pure solutions.

8.4. Conclusions

A simple kinetic model with only two unknown kinetic constants was proposed to

explain the growth kinetics of sucrose crystals in pure solutions. The proposed

kinetics incorporates the kinetic constant to explain the change in activity of

dislocation spirals on the crystal surface. The proposed model was obtained from the

basic expression of BCF thus enabling to determine the kinetic constant of the growth

process. The proposed model is very simple to use, however this approach is purely

kinetic approach disregarding the several complex mechanism which may occur

during the growth process due to the influence of supersaturation and temperature. No

arguments are put forward in this study about the complex mechanisms of the crystal

growth process, instead the approach was made simple to simultaneously explain the

effect of kinetics and the change in activity of the dislocation spirals.

149

8.5. References


Growth. 3-4, 331-334.

Bennema, P. and Gilmer, G.H. (1973). Kinetics of crystal growth in P. Hartman (Ed),

Crystal Growth: An introduction, North-Holland.

Berglund, K.A. (1980). Growth and size distribution kinetics for sucrose crystals in

the sucrose-water system, M.S. Thesis, Colorado State University, Ft. Collins,

1980.

Berglund, K.A. and Murphy, V.G. (1986). Modeling growth rate dispersion in a batch

sucrose crystallizer. Ind. Eng. Chem. Fundam. 25, 174-176


equilibrium structure of their surfaces. Philos. T. R. Soc. A. 1934, 299-358.

Ferreira, A., Faria, N. and Rocha, F. (2008). Roughness effect on the overall growth

rate of sucrose crystals., J. Cryst. Growth. 310, 442 – 451.

Garside, J., Philips, V.R. and Shah, M.B. (1976). On size-dependent crystal growth,

Ind. Eng. Chem. Fundam. 15(3), 230-233.

Lacmann, R., Herden, A. and Chr. Mayer. (1999). Kinetics of nucleation and crystal

growth., Chem. Eng. Technol. 22, 279-289.


Ouiazzane, S., Messnaoui, B., Abderafi, S, Wouters, J. and Bounahmidi, T. (2008).

Estimation of sucrose crystallization kinetics from batch crystallizer data. J.

Cryst. Growth. 310, 798-203.

Pantarakas, P., Flood, A.E. and Matsuoka, M. (2005). A new mechanism for crystal

growth rate dispersion: the effect of microscopic surface perfection on crystal

growth kinetics, 133-138, 16th international symposium on industrial

crystallization, International congress centre, Dresden, Germany, 11-14th

September 2005.

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Chapter Chapter Chapter Chapter 9999

Contributions of the present research and few suggestions Contributions of the present research and few suggestions Contributions of the present research and few suggestions Contributions of the present research and few suggestions

for future workfor future workfor future workfor future work

In the present study, we focused only on the effect of Hodag CB6, a non-ionic surfactant

on the growth rate and morphology of the sucrose crystals. The effect of the surfactant on

the surface free energy and on the created crystals is studied using Inverse Gas

Chromatography technique. It would be interesting and useful to know the influence of

the added surfactant on the viscosity of the sucrose solution, which will be helpful in

understand the influence of mass transfer on the growth process.

It was studied the influence of the surfactant on the morphology and

agglomeration, based on pseudo three dimensional parameters based on the two

dimensional images obtained via an offline image analysis technique. However the

generation of pseudo 3D parameters from 2D images is subjected to several limitations

and assumptions. These limitations could be avoided by adopting a stereo vision system

for online capture of growing crystals.

In this study, since the experiments are carried out in a batch crystallizer with

huge number of crystals growing inside the crystallizer, no attempts were made to study

the effect of added surfactant on distribution of dislocation activities of the sucrose

crystals as it is impossible to monitor each crystal individually. However for future work,

it would be interesting to perform experiments with limited number of crystals (may be in

a small chamber) to determine the distribution of dislocation activities of the sucrose

crystals in pure and impure solutions. All the suggestions made in this chapter may be

applicable to any crystals growing in pure solutions and also in presence of other

impurities.

Transfer of impurities into crystals in industrial processes: … · 2017-08-28 · Vasanth Kumar...

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Transcript of Transfer of impurities into crystals in industrial processes: … · 2017-08-28 · Vasanth Kumar...